Ms. Graham defeated Representative Ralph Norman, a hard-line conservative who has mostly backed Mr. Trump’s agenda in Congress but sometimes clashed with him on spending.

She will face Dr. Annie Andrews, the Democratic nominee, in November in a state that Mr. Trump won in 2024 by 18 points.

Before her brother’s death, Ms. Graham lived a quiet life with her family in the suburbs of Columbia, S.C. She had never before held elected office nor shown an interest in doing so. Even residents who lived in her own community said in interviews that they had hardly seen her around.

That all changed in July, when Governor Henry McMaster of South Carolina appointed her to serve out the remainder of her brother’s term in the Senate. At the time, she was considered a place holder while the special election played out to fill a full, six-year term. But a high-stakes meeting in the Oval Office convinced President Trump that Ms. Graham was the one for the more permanent job.

He endorsed her, personally called high-ranking Republicans in the state to urge them to do the same, and traveled to Myrtle Beach to rally on her behalf. A super PAC run by his advisers, MAGA Inc., notoriously wary to spend on races this cycle, invested nearly $800,000 on phone calls to urge voters to cast their ballots for Ms. Graham, according to campaign finance filings released on Monday, nearly a third of the total the committee has spent this cycle.

Her victory came in spite of a high-profile stumble at a televised debate last week, when she stumbled over a question about the strategic importance of Taiwan to the United States and said she was “not that informed on national security.” A clip of the gaffe went viral, magnifying voters’ concerns about whether she was experienced enough for the job.

Ms. Graham defended her performance, saying she was simply being honest about her status as a political outsider.

She also repeatedly told voters, in person and on Fox News, that she would govern differently than her brother. Mr. Graham, at the time of his death, had a complicated relationship with the state’s Republican base, which did not always favor his hawkish foreign policy positions nor his past support for comprehensive immigration reform.

Ms. Graham has said she will be more focused on domestic policy than Mr. Graham, for whom national security was a passion. She has also sided with Mr. Trump on issues where he and her brother disagreed, such as getting rid of the Senate filibuster and passing a voting restrictions bill called the SAVE America Act, which would require voters to present proof of citizenship to register to vote.