Dr. Amish Shah, a moderate Democrat, won a House primary in a battleground Arizona district on Wednesday, according to The Associated Press, defeating a centrist candidate supported by House Democrats’ campaign arm.

Dr. Shah, an emergency physician and former state lawmaker who proselytizes about the power of door-knocking, will face Jay Feely, the Republican nominee and a former journeyman N.F.L. kicker, in the general election.

Dr. Shah and Mr. Feely, whom President Trump backed in the primary, have some shared history: In 2008, Dr. Shah was a sideline physician for the New York Jets and Mr. Feely was the team’s kicker.

The two are racing to replace Representative David Schweikert, a Republican who decided to give up his seat to run for governor. The contest is expected to be one of the most expensive House races in the country in November, as Democrats look to capitalize on Mr. Trump’s unpopularity to win back control of the lower chamber of Congress.

Dr. Shah also ran for the seat in 2024, narrowly losing to Mr. Schweikert. The district surrounds Scottsdale and includes a part of Phoenix.

Dr. Shah’s primary victory on Wednesday over Marlene Galán-Woods, a former Republican and onetime broadcast journalist, represented the latest misfire by House Democrats’ campaign arm, the Democratic Congressional Campaign Committee.

At his election night party in Phoenix on Tuesday, Dr. Shah said he expected that if he won the primary — which had not yet been called — he would soon speak with leaders of the campaign committee.

“I hope that I can get their endorsement over Jay Feely,” he said, drawing laughter.

On Wednesday night, Representative Suzan DelBene of Washington State, chair of the campaign committee, said in a statement that Dr. Shah would “always put his community first.”

“Arizonans already know and trust Amish will work to make their lives more affordable, and that’s why they’ll enthusiastically elect him this November,” Ms. DelBene added.

The committee had poured money into the expensive primary race to try to elevate the moderate Ms. Galán-Woods, describing her on its website as “the straight-shooter Arizonans deserve.” She is the widow of Grant Woods, an Arizona attorney general and ally of John McCain who turned against the Republican Party over Mr. Trump.

House Democrats’ campaign arm has waded into several competitive Democratic races this year, spending on candidates who party leaders believe would be stronger general-election contenders in important races.

Although a number of the candidates the committee has backed have won their primaries, others have faltered: Moderate candidates backed by House Democrats’ campaign arm lost to progressives in battleground districts in northern Maine and in the Central Valley of California.

The intervention in favor of Ms. Galán-Woods in Arizona surprised some Democrats, who saw minimal ideological daylight between her and Dr. Shah.

Dr. Shah, for his part, assailed national Democratic leaders for the role they played in the race.

“Arizona voters do not want people from D.C. meddling and putting their thumb on the scale and telling voters who they should be picking,” he said in an interview. “That shouldn’t be happening.”

Representative Adelita Grijalva, a progressive Democrat from a neighboring district, agreed. In an interview, she said the result showed that House Democrats’ campaign arm needed to “stay out of primary elections.”

“I hope that this is a lesson,” Ms. Grijalva said.

Sejal Govindarao contributed reporting.