Marjorie Taylor Greene wins her primary, dashing establishment G.O.P. hopes.

Representative Marjorie Taylor Greene, whose far-right beliefs and confrontational behavior earned her opposition in both parties, won the Republican primary in her Northwest Georgia House district, beating a businesswoman who had garnered support among some in the G.O.P. establishment.

Ms. Greene’s victory over a crowded field dashed the hopes of some Republicans, who had believed the loss of Representative Madison Cawthorn, another far-right Republican, in a primary in North Carolina last week could start a pattern.

Money and endorsements had begun flowing to Ms. Greene’s chief opponent, Jennifer Strahan, a health care executive, and if Ms. Strahan could have held Ms. Greene under 50 percent, the race would have headed to a runoff election in which the challenger was likely to win additional mainstream Republican backing.

Ms. Strahan portrayed herself as the grown-up in the race. “We need to have public servants who are in policy, that are not chasing around the concept of being a celebrity,” she said in a recent video interview with Forbes, adding, “We need a serious representative.”

But Ms. Greene’s victory validated the loyalty of Representative Kevin McCarthy of California, the House Republican leader, who has told G.O.P. donors that Ms. Greene is simply a reflection of her conservative district.

Ms. Greene was elected in 2020 after espousing beliefs in line with the QAnon conspiracy theory and making numerous derogatory comments about Black people, Jews and Muslims. She has since tried to distance herself from her most inflammatory views.

Ms. Greene was stripped of her committee assignments by a House vote in February 2021 after it came to light that she had repeatedly endorsed calls on social media for top Democrats to be executed. And her candidacy for re-election was challenged by lawyers who accused her of backing an “insurrection” against the government with her sympathies for the rioters of Jan. 6.

The Democrat expected to prevail in the primary on Tuesday, Marcus Flowers, has amassed a huge war chest to take on Ms. Greene in the fall. His advertising might clutter the airwaves in Georgia’s 14th District, but few believe that such a Republican area could elect a Democrat in a year when even closely drawn districts are trending toward the G.O.P.