In her victory speech, Ms. Flanagan signaled that she would focus on the rising cost of living in the general election, and reveled in winning a primary in which she had been heavily outspent by Ms. Craig.

“For months now, I have been telling you that this campaign was about the many versus the money,” she said. “Well, guess what, the many just won.”

Ms. Craig, for her part, said she had called Ms. Flanagan to concede. “Peggy’s story is one of grit, of determination and resolve,” Ms. Craig said in a speech late Tuesday, adding, “To every person that supported me, I ask you tonight to support and elect Peggy Flanagan.”

The Minnesota primary was shaped by a backlash to the Trump administration’s immigration crackdown in the state last winter. Ms. Flanagan criticized Ms. Craig over a vote she made for one of Mr. Trump’s signature immigration policies — a move that the congresswoman said she had come to regret.

Ms. Flanagan, a member of the White Earth Band of Ojibwe, could become the first Native American woman to serve in the Senate if she wins the November general election.

She will face Michele Tafoya, a moderate Republican and a former N.F.L. sideline reporter, in a Democratic-leaning state that has sometimes sent Republicans to Washington in recent decades. Former Vice President Kamala Harris, whose running mate was Gov. Tim Walz of Minnesota, won the state by only four percentage points in the 2024 presidential election.

The winner of the Senate race will succeed Tina Smith, a Democrat, who is retiring.

Ms. Flanagan has said she plans to tie Ms. Tafoya to Mr. Trump, saying her Republican rival would be a “‘Yes Sir, Mr. President’ Senator.” Even before Tuesday, Ms. Tafoya, who was not endorsed by Mr. Trump, had begun to focus on Ms. Flanagan, casting her as a career politician and attacking her over a major fraud scandal in the state government’s social safety net programs.

Ms. Flanagan’s candidacy will offer another general-election test case of the left’s ability to win in competitive terrain. Her victory on Tuesday came a week after Dr. Abdul El-Sayed, a progressive former public health official, captured the Democratic nomination for Senate in Michigan, a pivotal swing state.

And it ended a bruising Democratic race in Minnesota. Ms. Craig argued that Ms. Flanagan had unique weaknesses as a general-election candidate, citing the fraud scandal.

Ms. Flanagan criticized Ms. Craig for accepting financial support from corporate and industry groups, including some with undisclosed donors.

Ms. Flanagan was backed by left-wing leaders including Senators Bernie Sanders of Vermont and Elizabeth Warren of Massachusetts. Locally, she was backed by Senator Smith and Representative Ilhan Omar, a progressive from Minneapolis.

Ms. Craig, who raised significantly more money than Ms. Flanagan, drew the support of establishment figures including Representative Hakeem Jeffries of New York, the Democratic House leader, and Representative Nancy Pelosi of California, the former speaker.

Senator Chuck Schumer of New York, the leader of Senate Democrats, did not publicly back a candidate.

Governor Walz, who was once mentored by Ms. Flanagan but has had a sometimes tense relationship with her in recent years, also stayed neutral. But his wife, Gwen Walz, endorsed Ms. Craig.

“We’ll all be on the same team come Wednesday morning,” Ms. Flanagan said in an interview on the eve of Primary Day.

Ernesto Londoño contributed reporting.