Mr. Ellzey, a state representative, was victorious in a runoff against Susan Wright, whose husband, Ron Wright, represented the Sixth Congressional District before he died of Covid-19.AUSTIN, Texas — The widow of a Texas congressman who died early this year of Covid-19 lost to a freshman state representative on Tuesday in a special runoff election between Republicans seeking to fill the vacant House seat.State Representative Jake Ellzey, who narrowly missed capturing the Republican nomination for the seat in 2018, defeated Susan Wright, whose husband, Ron Wright, died in February about two weeks after testing positive for the coronavirus. The Associated Press called the race after Mr. Ellzey had obtained 52.9 percent of the vote with 90 percent of precincts reporting.“Jake will be a strong and effective leader for the people of North Texas and he will fight tirelessly for their values in Washington,” Gov. Greg Abbott said in a statement.In May, Ms. Wright and Mr. Ellzey had each captured far below the 50 percent majority needed to avoid a runoff in a 23-way contest for the state’s Sixth Congressional District, which represents three counties just south of the Dallas-Fort Worth metropolitan region.In the end, the runoff election, which drew far fewer voters than the primary contest, was less about two ideologically similar candidates and more about how much sway former President Donald J. Trump would have in getting people to cast ballots for Ms. Wright, whom he endorsed before the primary.In a duel of former Republican leaders, Rick Perry, the state’s former governor and a cabinet member of Mr. Trump’s administration, threw his weight behind Mr. Ellzey, who like Mr. Perry is a former military pilot.The contest between Ms. Wright and Mr. Ellzey, who overtook a Democratic candidate by 347 votes to secure a slot in the runoff, disappointed Democrats, who had hoped to tap a reservoir of shifting demographics and Hispanic and African American growth in a district where Mr. Trump won by only three percentage points in November.Susan Wright greeted voters last week outside an early voting site in Arlington, Texas.Elias Valverde II/The Dallas Morning News, via Associated PressMr. Ellzey, 51, a Navy veteran, is in the middle of his first term in the Texas House of Representatives. Ms. Wright, 58, is a longtime Republican activist who pledged to continue her husband’s legacy on a host of conservative priorities, including abortion, guns and immigration.Both candidates supported the Republican-backed voter overhaul legislation in Texas, a measure that prompted Democrats to leave the state to block a vote just days into a special session. Now Mr. Ellzey will join the second-largest congressional delegation — 23 Republicans and 13 Democrats — in the U.S. House behind California.The so-called Trump Factor was the biggest subplot in Tuesday’s contest, with Ms. Wright and her supporters hoping the endorsement would propel her to victory. The former president retains an immense hold on Texas Republicans, and he carried the district by 12 points in 2016 before losing ground in the region to Joseph R. Biden Jr. last year.Ms. Wright, who entered the contest two weeks after her husband’s death, had prominently displayed the former president’s endorsement throughout her campaign and introduced Mr. Trump at a virtual election-eve rally on Monday night.The Club for Growth, a conservative fiscal organization that supported Mr. Trump in 2020, has also aligned with Ms. Wright, spending $1.2 million to fund ads and mailings attacking Mr. Ellzey’s legislative record and his conservative credentials, prompting fierce rebuttals.Although the two candidates share similar views on most of the base issues, the Club for Growth attacks injected a harsh tenor into the race, becoming an issue themselves. Mr. Perry, the former governor, described them as “junk” and “absolute trash” and demanded that Ms. Wright disavow the claims, which she refused to do.Joe Barton, who represented the district in Congress for more than three decades, said the tone of the Club for Growth ads was a factor in his decision to endorse Mr. Ellzey, though he was friends with the Wrights.Heading into Tuesday’s race, Mr. Ellzey had raised $1.7 million, far more than the $740,000 raised by Ms. Wright, according to news media reports. More