Ms. Gabbard adjusted her position on warrantless wiretaps of overseas communications. She promised not to oppose reauthorization of the measure, a key switch in time that reassured Senator Tom Cotton of Arkansas, the Republican chairman of the Intelligence Committee, and Senator Todd Young, Republican of Indiana and one of the fence sitters.

Kentucky Senator Mitch McConnell was the only Republican to vote against Gabbard, who faced scrutiny from lawmakers over her 2017 trip to Syria and dubious statements about the Russia-Ukraine war.

Gabbard, among President Donald Trump’s most controversial nominees, overcame the initial objections of a handful of Republicans skeptical about her qualifications.