Donald Trump was spared fresh political embarrassment on Tuesday when his favoured candidate won a Republican primary election in Ohio.

The coal lobbyist Mike Carey, endorsed by the former president, was on course for a comfortable victory over Ron Hood and Jeff LaRe in the state’s 15th congressional district with more than a third of the vote in a crowded field.

“Great Republican win for Mike Carey,” Trump said in an emailed statement. “Big numbers! Thank you to Ohio and all of our wonderful American patriots. Congratulations to Mike and his family. He will never let you down!”

The special election to replace Steve Stivers, who quit Congress to work in the private sector, had been billed as the latest test of the former president’s sway as a kingmaker among Republicans.

The primary field consisted of 11 contenders, some with more legislative experience and name recognition among conservatives than Carey.

LaRe, a state representative, had been endorsed by Stivers, while Bob Peterson was backed by the powerful political arm of Ohio Right to Life and the former senate president Larry Obhof. The state senator Stephanie Kunze had won the endorsement of the Republican party in the district’s biggest county, Franklin, and of the Value In Electing Women political action committee.

But none was able to thwart Carey in what Trump and his supporters are likely to see as political validation ahead of next year’s midterm elections.

Congresswoman Elise Stefanik of New York, a staunch Trump ally, said: “I was proud to join President Trump in endorsing Mike Carey, and I am thrilled to congratulate Mike on his hard-fought victory in a tough and crowded primary.

“Mike is a proven conservative fighter who would make a tremendous ally in our fight to combat House Democrats’ radical Socialist agenda. I look forward to Mike’s victory in November and to working together to help make America more prosperous and free.”

The former president was given a bloody nose last week when Susan Wright, the widow of Representative Ron Wright, lost a Republican primary in Texas to the state representative Jake Ellzey despite the ex-president’s endorsement. However, Democrats were able to vote in that election so Ellzey may have been boosted by protest votes.

Even so, a second defeat on Tuesday would have sparked renewed speculation about Trump’s waning influence over the party in general and congressional primaries in particular. In some cases his chosen candidates have not been able to match the fundraising of their rivals.

Ohio’s 15th congressional district includes the fast-growing southern suburbs of Columbus and the state’s second-biggest university, Ohio University.

On the Democratic side, the state representative Allison Russo, a health policy consultant, defeated Greg Betts, a former army officer and decorated combat veteran, for the nomination.

Russo said: “For far too long, working Ohioans in this district have not had someone in Congress who is willing to stand up to the special-interest politicians and lobbyists who run Washington. That needs to change.”

Winners of the August primaries will face off in the 2 November general election. Ohio, a classic swing state, voted for Trump in 2016 and 2020.