Tim Duncan and Matt Bonner scored 20 points apiece for the shorthanded Spurs, who learned earlier that guard Manu Ginobili and forward Tiago Splitter were expected to miss the next two weeks with injuries.
Richard Jefferson scored only five points, but three came on a long-range shot from the right corner that gave the Spurs a five-point lead in the last minute and all but sealed San Antonio's first 11-game winning streak since November 2010.
Al Jefferson led Utah with 20 points and 11 rebounds while Paul Millsap also had a double-double, scoring 16 and pulling down 11 boards. The Jazz have lost four of their last five and fell to 3-9 in their last 12.
"Tough loss. I thought our guys really played hard," said Jazz coach Tyrone Corbin, whose team had more rebounds, more points in the paint and more fast break points than the Spurs. "We had a chance to win the ball game."