The Spurs, who were eliminated by Memphis in the first round last year in a shocking upset, will now go on to meet the winner of the Memphis-Los Angeles Clippers series.
San Antonio drained 10 three-pointers in the victory, while Utah went 0-for-13 from long range in the contest.
Al Jefferson netted 26 points and grabbed 10 boards, while Derrick Favors added 16 and 10 for Utah.
Abigail Breslin wears sheer paneled gown for 'August: Osage County' premiere
Salvation Army bell ringer assaulted for saying 'Happy Holidays'