The Spurs faced a three-point deficit heading into the fourth period, during which they outscored the Jazz 31-15.
San Antonio improved to 9-1, the best record in the Western Conference and second in the NBA only to the thus far perfect mark put together by Indiana.
Utah has the worst record in the league with just one win in 10 games.
Derrick Favors scored 20 points and collected a career-best 18 rebounds for Utah.
Pregnant Mila Kunis wins 'Best Villain' at MTV Movie Awards
Charlize Theron not engaged to Sean Penn 'yet'