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.