Pierce had a chance to win it in regulation, but his 19-footer at the buzzer rimmed out.
Alec Burks' reverse layup pulled Utah to 108-105 with 37 seconds left in overtime. Kevin Garnett's banked 3-pointer with 13 seconds left came after the shot clock expired, giving the Jazz another chance.
Paul Millsap was fouled before he could get off a 3, but made two free throws with 4.2 seconds remaining.
Courtney Lee added two free throws at the other end with 1.2 seconds left to bump Boston's lead back to three, and Randy Foye's 26-footer at the buzzer missed everything.
Avery Bradley added a season-high 18 points for Boston.
Gordon Hayward led Utah with 26 points, Millsap had 16 and Al Jefferson finished with 15 points and 11 rebounds.
The Celtics (30-27) were playing their fifth game in seven days, but didn't seem to care down the stretch.
The Jazz (31-25) led 101-99 in overtime on DeMarre Carroll's 21-footer, but Pierce countered with a 3-pointer, then followed with a pull-up jumper over Carroll and a 15-footer to give the Celtics a 106-101 edge with 1:12 left.
Jefferson hit a 15-footer with 1:05 left to get Utah within 106-103, but Garnett's jumper over Jefferson helped seal it.
The Celtics also were smart down the
The Jazz trailed by eight entering the fourth but opened on a 13-2 run.
Jefferson's 10-foot turnaround jumper over Brandon Bass tied it at 93 with 2:46 left in regulation.
Pierce hit an 18-footer with Carroll diving at him for a 97-95 Boston lead with 36 seconds remaining in regulation, only to see Burks tie it with a tough layup with 19 seconds left.
The game took a 16-point swing in the third, as Boston trailed 58-50 only to counter with a 20-4 run and lead 80-72 entering the fourth.
Pierce ignited the run with a 3-pointer, Bradley hit two more 3s and Lee added a dunk after a steal and another 3-pointer. Pierce capped the run with a jumper over Hayward for a 70-62 Boston lead.
The Celtics hit 6 of 13 3-pointers in the quarter, while Utah made just 5 of 16 from the field.
Utah trailed 34-27 after Jason Terry's 3-pointer with 10:49 left in the second but went on a 17-2 run to lead 44-36 with 5:46 left in the quarter.
Utah led 53-48 at halftime.
The Celtics led 28-26 after the first in a quarter that saw seven lead changes and seven ties. Overall, the game had 13 lead changes and was tied 17 times.
NOTES; Jazz coach Tyrone Corbin opted to start Earl Watson over Jamaal Tinsley at point for a faster pace, but Burks ended up playing much of the game there. ... Jazz F Derrick Favors picked up his third foul with 9:06 left in the second quarter. . Jazz G Foye needed four 3-pointers to tie Mehmet Okur (129, 2006-07) for the franchise single-season record. Foye went 0-5 Saturday but hit his first Monday and finished 2 of 6 . . Bradley started 5 of 5 and had 10 points in six minutes for Boston, while Millsap started 4 of 4 for Utah.