Gov. Chris Sununu of New Hampshire is ideologically limber, a Republican who favors abortion rights but vetoed a bill banning firearms on school property. At 45, he is America’s youngest governor, and a member of a well-known political family. He is also seeking re-election in a state increasingly inhospitable to his party.

Gov. Roy Cooper of North Carolina is a mild-mannered Southerner who slipped into office in 2016 after a backlash over an anti-transgender rights law. He is a Democrat who has largely been thwarted by the Republican-led legislature, and is in search of a second term in a state with an energized Trump base.

Mr. Sununu and Mr. Cooper face two of the most competitive governor’s races in the country this year out of 11 on the ballot. But even as they paddle against the political currents, their handling of the coronavirus outbreak has won bipartisan support. As governors nationwide see their favorability rise for taking charge in a time of crisis, those facing voters in November may benefit beyond the usual blessings of incumbency.

In contrast to President Trump, whose approval bump during the health emergency has been modest by historic standards and is rapidly fading, governors are experiencing strong support for providing sober updates of new cases and hands-on guidance like how to apply for unemployment checks. Once dull gray figures to most voters, governors have emerged as political stars thanks to daily news conferences and the gravity of the health emergency. A Monmouth University Poll published Wednesday found that 72 percent of adults nationally thought their governors were doing a good job handling the virus.

“I think the governors are closer to the sun, closer to the voters; when you’re leading in a time of crisis it’s very relevant to them,” said Morgan Jackson, Mr. Cooper’s political strategist. The approval may diminish as the election heats up in October and voters retreat to their partisan corners, he said. “But governors are in a better position even than a United States senator and the president to take advantage of this time.”

In North Carolina, voters shared in interviews this week the anxieties of Americans everywhere, concerned about dwindling savings, long waits for small-business relief and unemployment benefits, and a lack of testing for the virus.

But even people who want to re-elect Mr. Trump praised Mr. Cooper’s stay-at-home order of March 27, which at the time was only the second by a Southern governor. On Thursday, he extended the social distancing mandate, limiting the number of people who can be in stores and placing restrictions on nursing homes.

“He’s doing everything in his power to keep everyone as safe as possible,” Matthew Greene, a political independent, said of Mr. Cooper. A small-business owner in Winston-Salem, who voted for Mr. Trump and is likely to again, Mr. Greene, 34, added: “I don’t think anybody’s thinking about who to vote for right now. They’re looking for answers and safety and whoever’s going to make them feel safe is who they’ll vote for.”

Polls show Mr. Cooper’s job approval has climbed to the mid-50s, up 10 points from the first three years of his administration, which counts as a healthy advantage in a state split down the middle politically.

Melissa Spurling, a behavioral therapist in rural Belwood, N.C., is a strong supporter of Mr. Trump’s but said that Mr. Cooper was doing a good job — because “he’s taking his lead from the president,” in her view. Mr. Trump first advised Americans to keep children home from school and avoid restaurants, unessential travel and gatherings of more than 10 people on March 16. That was 11 days before Mr. Cooper issued his more sweeping stay-at-home mandate backed by the power of law enforcement.

Ms. Spurling, 49, is open to voting for Mr. Cooper over his Republican challenger, Dan Forest, who has been largely eclipsed by the governor during the crisis. “I haven’t heard anything positive about him,” she said of Mr. Forest, who is the lieutenant governor. “At times like this you don’t really hear about other politicians except for the ones in office.”

In New Hampshire, a poll by the University of New Hampshire in mid-March showed only 41 percent of state residents approved of how Mr. Trump was handling the pandemic, but three out of four approved of Mr. Sununu’s handling of the crisis. The governor’s supporters crossed political lines, including 70 percent of independents and 61 percent of Democrats. This week the governor reversed his objections to widespread use of mail-in ballots and said the state would offer them to all voters requesting one in November.

“Sununu’s been ubiquitous in terms of giving good information and keeping calm and encouraging people to do takeout and stay home,” said Dave Carney, a Republican strategist in New Hampshire.

Partisan views of Mr. Trump, Mr. Carney added, are so hardened that even events as dramatic as the coronavirus outbreak and bitter arguments over whether the president adequately met the threat barely shift public opinion. By contrast, there is less partisanship around governors, who are seen as local problem-solvers.

Mr. Carney predicted 2020 would be a good year for incumbents up and down the ballot nationally because challengers will have a tough time breaking through to voters who are deeply concerned about their health and jobs, especially if there is a second wave of infections in the fall.

“It’s going to be hard to defeat an incumbent based on normal red and blue teams,” he said.

That may be good news for vulnerable Republican senators and Democrats in the House, who have shifted from traditional campaigning to Zooming town halls with health experts and intense constituent service around small-business loans and unemployment benefits.

All told, as many as nine incumbent governors will be on the ballot in November. The Cook Political Report, a nonpartisan handicapper, rates three of the Republicans and two Democrats as “solid” for re-election. Three Republicans, including Mr. Sununu, are “likely” to retain seats. There is one open governorship, in Montana, which Cook rates a tossup (while Utah’s open seat is a virtual lock to stay in Republican hands).

Mr. Cooper’s race in North Carolina is rated “lean Democrat,” the most competitive of all the incumbents’ contests.

His Republican opponent, Mr. Forest, is a social conservative who strongly backed a 2016 law that required people to use public bathrooms corresponding to the gender on their birth certificates. After it became a target of national ridicule and boycotts, Mr. Cooper made its repeal a top campaign issue. He narrowly defeated Gov. Pat McCrory, the only Republican governor to lose in 2016. The bathroom law, known as H.B. 2, was tossed out.

Many North Carolina voters split their tickets in 2016, voting for both Mr. Trump and Mr. Cooper because of opposition to the bathroom law or a desire to put a check on the Republican legislature. It is unknown how many of those Trump voters will stick with Mr. Cooper this year.

One of them, David Lindsay, a mortgage loan officer for a bank in Cabarrus County outside Charlotte, said he would “reluctantly, most likely” vote for Mr. Trump again. “I’m aware he’s an idiot and sticks his foot in his mouth, that’s no shock,” he said. “But I think a lot of the time he does have the United States’ best interest in mind.” He said Joseph R. Biden Jr., the presumed Democratic nominee, “seems to be stumbling and not knowing what he’s talking about a lot of the time.”

Mr. Lindsay, 37, was undecided about the governor’s race. “I do think Governor Cooper has done a pretty good job since he’s been in office,” he said, including his handling of the coronavirus. “I almost wish it would have been a little stricter. If this thing is as bad as everybody reporting it thinks, we have to nip it in the bud.”

In mid-March, Mr. Forest opposed an order by Mr. Cooper to close bars and restaurants to combat the virus, citing economic fallout. A spokesman for Mr. Forest declined an interview request, saying the candidate has paused campaign activities since the outbreak. “We will continue to monitor the situation and at some point will get back to basics,” the spokesman said.

North Carolina is unique among states this year because it is holding highly competitive races for governor, the Senate and the presidency.

Although the state has been losing terrain for Democrats in federal elections for a decade, demographic changes are nudging it toward tossup status. Sabato’s Crystal Ball, a nonpartisan political handicapper at the University of Virginia, moved North Carolina this month from leaning Republican in the presidential contest to a tossup. It noted that Mr. Biden has consistently lead Mr. Trump in state polling.

In the Senate race, Thom Tillis, a first-term Republican, is regarded as vulnerable. The Senate campaign finance arms of both parties plan to shovel more money into the race than any other in the country: $21.6 million on the Republican side and $16.6 million by Democrats.

The Tillis campaign hopes enthusiasm for Mr. Trump, whose approval rating of 50 percent in North Carolina is higher than the national average, sweeps along the senator. It is tying his opponent, Cal Cunningham, a former state lawmaker, to what it calls “radical, liberal” polices embraced by Democrats.

In a sign that nasty campaign ads are unlikely to disappear despite a health emergency, the state Democratic Party unearthed old footage of Mr. Tillis saying he had no problem with restaurants not requiring employees to wash their hands, for a suddenly relevant digital attack ad.

Since 2016, when Mr. Trump carried North Carolina by 173,000 votes, or 3.6 percentage points, demographic trends have been reshaping the state. Charlotte and the Raleigh-Durham region continue to draw college-educated job seekers from out of state, many of whom import blue-state values.

Mr. Jackson, the Democratic strategist, who is advising Mr. Cooper and Mr. Cunningham, said a threshold has been crossed since 2016, with a majority of North Carolina voters in his internal surveys saying for the first time they did not live in the state 20 years ago — either because they have been born since then or moved in from elsewhere.

In the March 3 primary, Democratic voters under 40 outnumbered younger Republicans by four to one, according to statistics compiled by J. Michael Bitzer of Catawba College. The imbalance needs to be taken with a grain of salt since there was no competitive Republican presidential primary. Still, Mr. Bitzer, a professor of politics and history, said, “I think 2020 could be the tipping year.”

He offered an addendum familiar to pundits: “It all depends on turnout.”