No issue dominated the race more than public safety, as poll after poll showed combating crime was the most important issue to New York Democrats.

Sparse public polling suggested that Mr. Adams, a former police captain who challenged misconduct from within the system — part of a complex career — attained credibility on that subject in the eyes of some voters, which will have been a crucial factor if he wins, along with significant support from labor unions and deep ties to core Democratic constituencies.

But Ms. Wiley, a former counsel to Mr. de Blasio, repeatedly challenged Mr. Adams from the left on policing matters, expressing skepticism about adding more officers to patrol the subways and calling for greater investments in the social safety net and less in the Police Department budget. With a pitch centered on how to “reimagine” a more equitable city, she emerged as a favorite of left-wing leaders and progressive voters. She also had the backing of the city’s largest union, and of Representative Hakeem Jeffries, the state’s highest-ranking House Democrat — important factors in her effort to build a multiracial coalition.

“I’m feeling a lot of excitement and emotion from people about the historic nature of this race,” said Ms. Wiley, who would be the first Black woman elected mayor of New York, as she campaigned in Harlem.

Mr. Yang, who would be New York’s first Asian American mayor, and Ms. Garcia, a former sanitation commissioner, shared Mr. Adams’s criticisms of efforts to scale back police funding, and those three candidates also frequently addressed quality-of-life issues across the city. But they had divergent campaign messages in other ways. Mr. Adams branded himself a blue-collar candidate focused on issues of public safety and justice; Mr. Yang, who has no city government experience, cast himself as a fresh-thinking political outsider; and Ms. Garcia sought to seize the mantle of competent manager in the race.

“You have to win,” Elfrain Rodriguez, 74, told Ms. Garcia during a campaign stop in the Bronx.

“I’m working on it,” she said.

But if the race was defined in part by clashes over policy and vision, it also had all the hallmarks of a bare-knuckled brawl. Mr. Adams faced intense criticism from opponents over transparency and ethics, tied to reports concerning his tax and real estate holding disclosures and fund-raising practices. And Mr. Yang stumbled amid growing scrutiny of his knowledge of municipal government as rivals sharply questioned his capacity to lead.