In addition to losing a 12-point, third-quarter lead and the game, the Celtics saw superstar Kevin Garnett leave the court with a knee injury in the second quarter. Garnett sat out the rest of the game with what Boston officials said was a mild sprain.
With the game tied, Harpring hit a jumper from the free throw line with 1:11 to play. Harpring then grabbed the rebound on a miss by Leon Powe and Williams' fadeaway jumper with 27 seconds to go gave the Jazz a four-point advantage.
Utah closed the game on an 8-2 run to win its third in a row. The Jazz shot 56 percent from the field in the second half after hitting only 29 percent in the opening two quarters.
Mehmet Okur led the Jazz with 19 points and Williams had 18. Paul Pierce scored 20 for the Celtics.
Boston has only a one-game lead over Cleveland in the race for the best record in the Eastern Conference.