Jim Pillen, a University of Nebraska regent backed by the state’s powerful Ricketts political machine, has won the Republican primary for Nebraska governor, defeating a scandal-marred millionaire who had the backing of former President Donald J. Trump.

The Associated Press declared Mr. Pillen the winner over his main rivals, Charles W. Herbster, a Trump-endorsed agribusiness executive who funded his own campaign and, in the race’s final weeks, was accused of groping women, and Brett Lindstrom, a state senator who appealed to the moderate wing of the party.

Mr. Pillen’s victory makes him an overwhelming favorite to become Nebraska’s next governor in November. Democrats have not won a statewide election since 2006. The party nominated Carol Blood, a state senator from the Omaha suburbs.

Mr. Herbster is the first candidate endorsed by Mr. Trump to lose a Republican primary in 2022. Many more Trump-endorsed candidates are facing stiff headwinds in coming primaries, starting with contests for governor in Idaho next week and in Georgia on May 24.

Mr. Pillen, in his victory remarks in Lincoln, pledged to run an administration focused on education and agriculture, two pillars of the state. He said he would promote Nebraska to both attract new residents and keep young people from leaving for other states.

“We all agree, we’re all in unison, we never ever, ever, give up on kids,” he said. “We’re going to invest the farm in our kids, so all of our kids know, the grass is greenest in Nebraska.”

Mr. Pillen, 66, ran a campaign predicated on the idea that Nebraska Republicans were satisfied with the administration of Gov. Pete Ricketts, his main political benefactor and most prominent supporter, who is stepping down because of term limits. Mr. Ricketts spent millions on television advertising backing Mr. Pillen while attacking Mr. Herbster and Mr. Lindstrom.

Once Mr. Herbster began to gain traction in the race, the mild-mannered Mr. Pillen adopted some of his rival’s right-wing positions on social issues. He sought to bar the teaching of critical race theory in the University of Nebraska system and came out against allowing transgender athletes from competing in high school girls’ sports in the state.

Mr. Pillen, a former defensive back for the University of Nebraska’s football team, became a highly successful veterinarian and pig farmer in the state. In addition to Mr. Ricketts’s backing, he had endorsements from a handful of the state’s most prominent figures, including Tom Osborne, his college football coach, who was also a three-term member of Congress from western Nebraska, and the comedian Larry the Cable Guy, who was raised on a farm in the state’s southeastern corner.

Much to the frustration of his opponents, Mr. Pillen skipped all of the televised debates during the primary campaign, opting instead to hold hundreds of small meetings with voters across the state. Mr. Pillen’s opponents argued that he lacked charisma and was not prepared to discuss the state’s issues; Mr. Pillen said he was building coalitions away from the prying eyes of the news media.

Mr. Lindstrom sought to rebuild the type of Republican coalitions that existed before Mr. Trump’s rise. He appealed to educated professionals in the state’s urban centers of Omaha and Lincoln and put political distance between himself and Mr. Trump — saying that the 2020 election was legitimate and that he would prefer “a new face” to lead the Republican Party in 2024.

While Mr. Lindstrom made a late charge in the polls, most of the race became a proxy fight between Mr. Ricketts and Mr. Trump, to whom Mr. Herbster yoked his political identity. He talked like Mr. Trump, adopted many of Mr. Trump’s policy positions and pledged to drain “the swamp” in Lincoln, the state capital.

In other Nebraska races, Mike Flood, a state senator from Norfolk who owns radio and television stations across the state, won the Republican nomination to the Lincoln-based congressional seat vacated by former Representative Jeff Fortenberry, who resigned after he was convicted of lying to the F.B.I. in a campaign finance investigation.

Mr. Flood defeated Mr. Fortenberry, who remained on the ballot but did not mount a campaign, and Curtis Huffman, an accountant.

Democrats in Omaha nominated Tony Vargas, a state senator, to face Representative Don Bacon, a moderate Republican who is seeking his fourth term. Mr. Vargas, the son of immigrants from Peru, is a former public-school teacher in Omaha who served on the city’s school board before he was elected to the Nebraska Legislature.

The House Democrats’ campaign arm is optimistic Mr. Vargas can be competitive in November, despite the difficult national environment for the party.

Mr. Bacon is one of 10 House Republicans who hold a district carried by President Biden in 2020. But in the last two elections, Omaha Democrats nominated Kara Eastman, a democratic socialist who did not appeal to centrist voters in the district. Mr. Vargas has not campaigned on the left-wing issues Ms. Eastman promoted.