The Jazz tied the game on a jumper by Al Jefferson with 1:56 to play and Utah did not score again.
Boston won its third in a row while Utah had a two-game winning streak snapped. The Jazz are halfway through a four-game eastern trip with stops remaining in Philadelphia and Washington.
Garnett was fouled with 1:08 to play and he made 1-of-2 shots from the line. Pierce hit two free throws with 18 seconds to play and Garnett added two more with 7 seconds left.
Utah missed its last seven shots and wound up with a 39 percent shooting performance to 50 percent for the Celtics.
Paul Millsap had 20 points and 12 rebounds for Utah, which has gone 1-5 on the road to open the season.