Jeff Green and Leandro Barbosa each scored 16 points for the Celtics, who won for the fifth time in six games. Kevin Garnett added 11 points and eight rebounds.
Boston's Rajon Rondo had 10 assists before leaving the game for good in the third quarter with a right ankle injury. It was his 32nd straight game with 10 or more assists. He was on the bench for the final quarter.
Paul Millsap led the Jazz with 20 points and 12 boards. Al Jefferson had 13 points and 14 rebounds.
Mo Williams missed three shots in the closing minute for Utah, which fell to 1-5 on the road. The Jazz won a triple-overtime game in Toronto on Monday.
The Celtics grabbed a 94-93 edge when Garnett hit the second of two free throws with 1:08 left. After Williams missed a long jumper and Gordon Hayward the follow on an attempted put-back, Garnett missed a jumper and Jefferson grabbed the rebound.
The Jazz called timeout with 33 seconds remaining and Williams missed on a left-handed scoop shot with 22 seconds to go. The Jazz fouled Pierce and he nailed both free throws, making it 96-93.
Millsap then missed a drive, but Boston's Green was called for traveling after grabbing the rebound, giving the Jazz one last shot. Williams missed another long jumper. Garnett sealed it with two free throws.
Boston led 93-88 after Green's three-point play with 3:40 left, but Jefferson scored the next five points, tying it on a jumper from the right wing with 1:21 to play.
Garnett's no-look, behind-the-back pass set up Barbosa for an easy layup midway into the final quarter, giving Boston an 80-74 lead. The teams then traded baskets before Green drove the lane for a dunk over Al Jefferson, bringing most of the crowd to its feet. He was given a technical, though, for taunting him on the play.
But despite the highlight baskets, the Jazz stayed close, narrowing it to 88-86 on Jefferson's layup with 4 1/2 minutes to play.
Rondo came up limping on a drive to the basket with 4:55 in the third, left the game and headed to the locker room about a minute later. He returned to the bench to loud cheers from the crowd with under a minute left in the third. The Celtics announced that he ''rolled'' his right ankle.
Pierce missed 10 of his initial 13 shots before hitting three straight 3s in a 1:17 span midway into the third quarter, with Rondo getting assists eight, nine and 10 on the baskets. Pierce scored 15 in the quarter on 5-of-9 shooting and Hayward scored 10 for Utah.
After Pierce's long-range shooting exhibit, Barbosa drove to the basket and scored six of the points in Boston's 8-0 run that gave the Celtics a 68-60 edge.
The Jazz then scored 10 of the final 15 points in the quarter, closing it to 73-70 at the break.
Utah continues its 4-game road trip Friday night at Philadelphia.