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.