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One explanation for her success is Ms. Wu herself, who is difficult to caricature as a radical.

Over her four terms as a city councilor, Bostonians have gotten to know Ms. Wu as soft-spoken and thoughtful, intensely focused on policy, meticulous about showing up at meetings and returning phone calls. That experience acted as a “buffer,” if any was needed, “for someone this progressive to be elected mayor,” said David Paleologos, director of the Suffolk University Political Research Center.

“That kind of quiet, methodical style is a new style for progressives,” he said. “It’s a different kind of style that she has invented.”

Lydia Chim, 26, a budget analyst who moved to Boston from California, said Ms. Wu struck her as experienced and practical, qualities she does not always find in progressives.

“It’s a refreshing thing to see a progressive candidate who really knows how to get things done,” she said.

Ms. Wu also cultivated relationships with the city’s conservative power centers, tapping into her Harvard pedigree and post-college experience as a management consultant and small-business owner. She comes across as “somebody who is very clearly into managing systems,” which has helped her build trust in those parts of the city, said Jonathan Cohn, the chair of a local Democratic committee and a progressive activist.

“Her career is where it is because she has done a good job of catering to business owners and progressives at the same time,” he said.

Ms. Wu has also benefited from some conditions outside her control.

The demographics of Boston are changing rapidly, with young professionals drawn to the city for jobs in technology, medicine and education. Boston has become “an intellectual elite city,” said Nan Whaley, the mayor of Dayton, Ohio, and the president of the U.S. Conference of Mayors. Its politics, she said, are changing accordingly.