Gov. Andrew M. Cuomo took a decisive step toward a third term on Thursday, quelling a liberal rebellion by turning aside the insurgent challenge of Cynthia Nixon to claim the Democratic nomination in New York.

Mr. Cuomo had marshaled the support of nearly all of the state and country’s most powerful Democratic brokers — elected officials, party leaders, labor unions and wealthy real estate interests — to defeat Ms. Nixon, beating her by 30 percentage points.

The race cemented both Mr. Cuomo’s standing as an unmatched force in New York politics and a merciless tactician with little regard for diplomacy.

Ms. Nixon had cast her first-time candidacy as a fight for the direction of the Democratic Party in New York and beyond, offering a pure brand of liberalism against Mr. Cuomo’s more triangulating pragmatism, a style defined less by ideology and more by what he deemed possible.

In the end, the governor’s record of achievements — on gun control, gay marriage, the minimum wage, paid-family leave and more — and his gargantuan fund-raising advantage spoke louder than Ms. Nixon’s objections over legislation he sidelined in the byzantine corridors of Albany’s capital.

The race was called about 30 minutes after the polls closed, with Mr. Cuomo watching the results roll in over dinner with senior staff at the Governor’s Mansion in Albany. Mr. Cuomo never appeared publicly after the polls closed on Thursday, letting the results speak for themselves.

Ms. Nixon called to offer Mr. Cuomo a private concession before a fiery speech before her supporters in Brooklyn, where she and her two insurgent allies for statewide office, Zephyr Teachout and Jumaane Williams, had gathered. All three lost.

In the attorney general’s race, Letitia James, the New York City public advocate and Mr. Cuomo’s choice, won the Democratic nomination in a four-way race, with Ms. Teachout finishing second. Should Ms. James prevail in November, she would become the first black woman to ever hold statewide office in New York. In the lieutenant governor’s race, Kathy Hochul, Mr. Cuomo’s running mate, fended off a challenge from Mr. Williams, a New York City councilman, winning by the narrowest margin of the three.

The lone bright spot for liberal insurgents came down ballot, where Democratic challengers in State Senate contests had knocked off six of the eight members of a group of rogue Democrats who had broken with the party in recent years to form a coalition with Republicans in Albany.

Mr. Cuomo’s victory ensures that no Democratic governor or senator in America lost a party primary in 2018, a sign of how steep a climb Ms. Nixon, an actress and activist, had faced, even before the governor’s campaign unloaded a sum close to $25 million to blanket the contest in a blizzard of television ads and glossy mailers.

“When others were underestimating us, he did not,” Ms. Nixon said in her concession speech. “And he spent accordingly.”

In November, Mr. Cuomo, 60, will seek to match the three terms that his father, Mario M. Cuomo, achieved as governor. He has forcefully denied any presidential ambitions of his own, saying the only way he would not serve through 2022 would be death.

Mr. Cuomo himself had sought to mostly ignore Ms. Nixon in recent months, focusing repeatedly on President Trump. His campaign, meanwhile, methodically pushed to undermine Ms. Nixon’s credibility in often-caustic terms, tapping into the concerns of New York Democrats that an experienced governor is needed while a hostile Republican occupies the White House.

After a six-month slog versus Ms. Nixon, Mr. Cuomo now faces a less than 60-day sprint of a general election against the Republican, Marcus J. Molinaro, the affable Dutchess County executive who was once the youngest mayor in the nation. He, like Ms. Nixon, is expected to be drastically outspent by Mr. Cuomo. And in a heavily Democratic state in what most strategists predict will be a Democratic year, Mr. Molinaro’s bid is not seen as a top-tier race for Republicans nationally.

The final margin in the primary belied the ferocity of the campaign, which began with the charge that Ms. Nixon was an “unqualified lesbian” by a top surrogate for Mr. Cuomo and ended with a mailer accusing her of silence on anti-Semitism. Mr. Cuomo called it “inappropriate” but did not apologize.

“He won ugly,” said Bradley Tusk, who served as campaign manager for former Mayor Michael R. Bloomberg.

Even before the polls had closed, there were worried whispers from New York City to Albany of those who had crossed him readying for a coming retribution tour.

When Ms. Nixon burst onto the political stage in March, it was as if she had unleashed the repressed id of New York progressives long frustrated with Mr. Cuomo’s transactional ways. But for many voters, Ms. Nixon never successfully presented enough evidence that she was prepared to be governor, other than offering what she was not: an Albany insider or Mr. Cuomo.

“If you run an outsider campaign, you have to run a campaign like Trump did, saying ‘Things are so bad that you’ve got nothing to lose, so who cares that I don’t have experience,’” Mr. Tusk said. “In this case, the guy with experience gets a lot done.”

She had roughly one-third of the vote, almost the same showing as Ms. Teachout had four years ago.

Still, in losing, Ms. Nixon arguably made as much of a policy impact on New York as some elected officials have: Mr. Cuomo embraced a series of liberal ideas soon after her entry, including moving toward legalizing marijuana, extending voting rights to parolees and brokering a deal to dissolve the Independent Democratic Conference, the group of Democratic state senators who had aligned with Republicans in Albany.

Among the six I.D.C. members who lost primaries on Thursday was their leader, State Senator Jeffrey D. Klein in the Bronx, who was defeated by Alessandra Biaggi, the granddaughter of Mario Biaggi, a former congressman.

While Ms. Nixon scored a record number of small donors for a New York race, she struggled to collect larger donations, pulling in a total of just under $2.5 million with about 10 days left in the race.

That is roughly how much Mr. Cuomo raised in a single day, at his birthday fund-raiser last December.

Turnout in 2018 was two and a half times larger than in 2014, even as Mr. Cuomo carried the state by nearly the same margin. It was a sure sign of his grip on the state that he could earn commanding victories in years with both large and small turnouts.

Mr. Cuomo was a no-show at the victory gala that his state party was throwing in Manhattan, where attendees snacked on baked oysters, pita, hummus and “pigs in blankets” amid chants of “four more years!” (One rogue supporter shouted “2020!”)

Mr. Cuomo seemed to stumble across the finish line in the final days of this race, dogged by questions of the timing of a bridge opening and the mailer that incorrectly sought to link Ms. Nixon to anti-Semitism.

But it didn’t matter.

Mr. Molinaro has used both issues to hammer Mr. Cuomo in some of the opening salvos of the fall campaign.

For now, Ms. Nixon is still technically on the November ballot as the Working Families Party nominee. She must decide whether to withdraw, and if so, the party, which spent much of the year at war with Mr. Cuomo, must decide whether to grant its line to the incumbent governor. Ms. Nixon declined to discuss her plans in a radio interview on Tuesday.