Katie Britt, a former chief of staff to the retiring Senator Richard C. Shelby of Alabama, won the Republican nomination to replace her onetime boss on Tuesday, comfortably defeating a right-wing rival in a race that puts the 40-year-old on track to become the youngest woman in the United States Senate.

The Alabama Senate primary was the marquee contest on Tuesday as a handful of states across the South held primaries or runoffs, and a House race in Texas last month that went to a recount gave a moderate Democratic incumbent a victory.

The Senate race in Alabama took a number of twisting turns involving former President Donald J. Trump, who has made the 2022 primary season into a rolling referendum on his influence. Mr. Trump has carefully guarded his record in picking Republican primary winners, and his shifting allegiances in Alabama were among the best examples of his obsession with scoring wins — and avoiding losses — ahead of a 2024 presidential run that he continues to loudly tease.

Yet even in races where Mr. Trump’s handpicked candidates have faltered this year, those who defeated them in primaries have rarely broken with the former president. Many have run as Trump allies even without his formal support.

In Alabama, Mr. Trump had initially offered his “complete and total endorsement” to Representative Mo Brooks, a congressional ally who spearheaded efforts to overturn the 2020 election and who spoke at the Jan. 6, 2021, rally near the White House that preceded the riot at the Capitol.

But when Mr. Brooks sank in the polls, Mr. Trump rescinded that endorsement leading up to the first round of voting in May. The former president claimed it was because Mr. Brooks had stopped fully embracing his falsehoods about the 2020 election. In the end, Mr. Trump backed Ms. Britt, who cuts a more traditional Republican profile as a former congressional staffer, lobbyist and past president of the Business Council of Alabama.

Ms. Britt, who lobbied privately for the endorsement, finished far ahead in the May primary, with almost 45 percent, nearly enough to avoid a runoff. She was a heavy front-runner in polls when Mr. Trump endorsed her earlier this month.

“Alabama has spoken,” Ms. Britt declared in a victory speech in Montgomery, Ala., on Tuesday evening. “We want new blood.”

Ms. Britt added that she entered the race despite naysayers telling her: “You’re too young. Wait your turn.”

Mr. Trump has scored a number of decisive wins in 2022 Senate primary races: Dr. Mehmet Oz in Pennsylvania, J.D. Vance in Ohio, Herschel Walker in Georgia and Representative Ted Budd in North Carolina. He has fared more poorly in governor’s races, losing in Georgia, Idaho and Nebraska. In the Pennsylvania governor’s race, like in the Alabama Senate contest, Mr. Trump made a late endorsement of a front-runner to claim a political victory.

More than $41 million was spent on television advertising in the Alabama race, with about twice as much spent on ads backing Ms. Britt as Mr. Brooks, according to AdImpact, a firm that tracks ad spending.

Ms. Britt ran as a Christian conservative, with the cross on her necklace clearly visible in a number of her television ads, including one she filmed at the border as she pledged to “fight to finish President Trump’s wall.”

Without Mr. Trump’s backing, Mr. Brooks campaigned against Senator Mitch McConnell, the Senate Republican leader, saying Mr. Trump was “conned” by the Kentucky Republican and accusing Mr. Trump of disloyalty. He held his election-night party at an indoor shooting range in Huntsville, Ala., on Tuesday and he was not in a charitable mood.

“The voters have spoken, but not spoken wisely,” Mr. Brooks said, adding of the groups that spent money for Ms. Britt, “I’m not pleased about congratulating these special interests but they rule Montgomery. They rule Washington, D.C. They rule the policy debate.”

In Georgia and Virginia, voters helped determine the Republican Party’s direction in a number of key congressional contests, setting up closely watched matchups for November. And in Washington, D.C., Mayor Muriel Bowser defeated three primary opponents in her bid to become the first mayor in the nation’s capital since Marion Barry in the 1990s to win three consecutive terms.

In Texas, a fierce Democratic clash in the border region of Laredo was called on Tuesday nearly a month after the May 24 runoff, as Representative Henry Cuellar, a moderate, survived a second consecutive primary challenge from Jessica Cisneros, a lawyer who was once his intern. A recount by the Texas Democratic Party found Mr. Cuellar won by 289 votes.

For Mr. Trump, Georgia has proved to be his most challenging state in 2022.

Gov. Brian Kemp, a Republican whom Mr. Trump had made a top target for defeat because he certified the 2020 election, won renomination in a landslide last month, easily dispatching a Trump-backed challenger. That same night, the former president saw his choices for secretary of state, insurance commissioner and attorney general in Georgia all defeated by Republican incumbents aligned with Mr. Kemp. Mr. Trump’s picks for lieutenant governor and U.S. Senate did win open races in May.

But on Tuesday, two of Mr. Trump’s picks for House races lost in Georgia.

In Georgia’s 10th District, Vernon Jones — a longtime Democrat who endorsed Mr. Trump in 2020, became a Republican and now calls himself a “Black Donald Trump” — lost to Mike Collins, the son of a former congressman, in a contest that became notably nasty.

The Collins campaign handed out rape whistles with Mr. Jones’s name on them to draw attention to a specific 2005 allegation and a history of misconduct with women. Mr. Jones filed a police report against Mr. Collins, claiming a tweet was threatening.

In the redrawn Sixth District, which is currently held by a Democrat but was redrawn into a Republican seat, Jake Evans, a lawyer, lost to Rich McCormick, a physician. Mr. Trump backed Mr. Evans, the son of a former ambassador appointed by Mr. Trump.

But Mr. Trump’s personal defeats were not necessarily a sign that the party base was in any way ready to break from his broader movement. Mr. Collins, for instance, ran as a “pro-Trump” Republican and a McCormick ad called him an “always America First” candidate.

The former president chose to stay out of a closely watched third Republican primary in the southwest corner of Georgia. Jeremy Hunt, a 28-year-old veteran who has drawn national support as a young Black Republican, conceded late Tuesday to Chris West, a member of the Georgia Air National Guard. The result was seen as an upset, after Mr. Hunt had raised 10 times as much as Mr. West and had finished in first place in the first round of balloting last month.

Mr. West will now face Representative Sanford Bishop Jr., a Democrat whom Republicans see as vulnerable this fall.

Also in Georgia, State Representative Bee Nguyen won the Democratic nomination for secretary of state over Dee Dawkins-Haigler, a former state lawmaker. Ms. Nguyen had finished first in the primary and had since secured the endorsement of Stacey Abrams, the Democratic nominee for governor.

Ms. Nguyen will face Georgia’s Republican secretary of state, Brad Raffensperger, who turned back a Trump-inspired primary challenge in May and was a star witness at the Jan. 6 hearing in Washington on Tuesday as he testified about his role opposing Mr. Trump’s efforts to overturn the 2020 election. Despite his actions refusing to bend to Mr. Trump, Democrats are targeting Mr. Raffensperger in the fall for his support of more restrictive voting laws in the state.

In Virginia, Republicans picked their nominees in two House races where the incumbent Democrats — Representatives Abigail Spanberger and Elaine Luria — are vulnerable because of the national political environment and new district lines.

In Ms. Luria’s seat, which is based in Virginia Beach and became less Democratic in the remapping, national Republicans backed State Senator Jen Kiggans, who defeated Jarome Bell, a Navy veteran. Mr. Bell had received a late boost from an ad that appears to be a Democratic-backed effort to elevate a nominee whom Democrats believe could be more easily defeated in November.

Mr. Bell, who has denied the legitimacy of the 2020 election, called for audits of all 50 states and to “execute all involved” in election fraud.

In Ms. Spanberger’s seat, Yesli Vega, a Prince William County supervisor who was endorsed by Senator Ted Cruz of Texas, finished first in a six-way primary, setting up what is expected to be a hotly contested race this fall.

Ms. Spanberger and Ms. Luria, who sits on the House committee investigating the Jan. 6 attack, were elected in 2018, the first midterm election under Mr. Trump, when Democrats were swept into power. Now they are seeking to survive in 2022, as polls point to signs of backlash against Democrats and President Biden.

Glenny Brock and Deborah Storey contributed reporting.

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