Tom Suozzi, a former Democratic congressman, won a closely watched special House election in New York on Tuesday, narrowing the Republican majority in Washington and offering his party a potential playbook to run in key suburban swing areas in November.

His victory in the Queens and Long Island district avenged a year of humiliation unleashed by the seat’s former occupant, George Santos, and stanched a trend that had seen Republicans capture nearly every major election on Long Island since 2021.

Mr. Suozzi, 61, fended off the Republican nominee, Mazi Pilip, in a race that became an expensive preview of many of the fights expected to dominate November’s general election, especially over the influx of migrants at the border and in New York City.

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