Eric Schmitt defeats Eric Greitens to win Missouri’s G.O.P. Senate primary.

Eric Schmitt, the Missouri attorney general, easily captured the Republican nomination for an open Senate seat on Tuesday, according to The Associated Press. His decisive victory derailed the political comeback of former Gov. Eric Greitens, whose campaign had been clouded by allegations of domestic abuse, infidelity and corruption.

Mr. Schmitt, a former state senator and treasurer, made a turn to the hard-right in order to fend off his top rivals, Mr. Greitens and Representative Vicky Hartzler, a longtime social conservative who was in second place as votes were counted Tuesday night, with Mr. Greitens trailing behind.

Mr. Schmitt had the backing of Senator Ted Cruz of Texas — which he parlayed into multiple appearances on Fox News — and a semi-endorsement from former President Donald J. Trump, who, unable to make up his mind, endorsed “Eric” on Monday without specifying which one.

His victory was a relief for Republicans in Missouri and in Washington, who had worried that nominating Mr. Greitens, four years after he resigned his governorship in disgrace to avoid impeachment, would put at risk a seat they hoped to pass easily from retiring Senator Roy Blunt to a Republican successor. Once a swing state, Missouri has become reliably red over the past decade.

If Mr. Greitens had won, Democrats planned to attack him on a record that included allegations from his former wife that he had physically abused her and one of their young sons, as well as accusations of sexual abuse from a hairdresser who said that he had lured her to his home, tied her up, torn off her clothes, photographed her partly naked, threatened to release the pictures if she talked and coerced her into performing oral sex.

“I’m hoping and praying that it is God’s will that Eric Greitens does not get the nomination, but if Eric Greitens wins the nomination, we will lose a Senate seat to the Democrats,” Rene Artman, the chairwoman of the St. Louis County Republican Central Committee, said days before the election. She had pleaded with Missouri Republican officials to more forcefully oppose Mr. Greitens.

A super PAC in Missouri funded by affluent donors in and out of the state attacked Mr. Greitens in advertising that used his former wife’s allegations as well as footage from a trip he took as governor to China, in which he appeared to speak positively about the country.

Mr. Greitens said the allegations against him were false and orchestrated by Washington Republicans such as Mitch McConnell, the Senate minority leader, and Karl Rove, the political chief of the George W. Bush White House. Mounting a campaign saturated in violent imagery, Mr. Greitens ran advertising featuring military-style assaults against “RINOs” — Republicans in name only — and shots of himself, a former Navy SEAL, firing high-powered weaponry.

In the end, Mr. Schmitt benefited from a highly fractured field of Republicans, 21 in all. It included Representative Billy Long, who claimed to be the true voice of Mr. Trump, and Mark McCloskey, a personal injury lawyer who made headlines when he and his wife brandished guns at Black Lives Matter protesters in front of the couple’s St. Louis home.

Ms. Hartzler was backed by Missouri’s junior senator, Josh Hawley, but snubbed by Mr. Trump, who told his supporters on his social media site, “I don’t think she has what it takes to take on the Radical Left Democrats.” Mr. Trump called Mr. Greitens “tough” and “smart” in an interview on the pro-Trump network One America News, and his son Donald Trump Jr. shot automatic rifles with Mr. Greitens at a shooting range and said on camera that they were “striking fear in the hearts of liberals everywhere.”

With Ms. Hartzler dismissed by the former president and Mr. Greitens under concerted attack from wealthy Republicans, Mr. Schmitt was able to prevail.