The Jazz jumped on the Celtics early and held on with Boston making it a four-point game with 5:25 left. Williams scored 13 of his 32 points in the fourth quarter and paid the price when Kendrick Perkins clobbered him on a flagrant foul with 2:54 to play.
The Celtics' winning streak had been their longest since 1986; Boston also owned an 11-game home winning streak. The Jazz joined Detroit, Charlotte, Washington and Toronto as the only teams to beat Boston at the TD Banknorth Garden this season.
Midway through the fourth quarter, Williams hustled back on defense after missing a jumper to steal a James Posey pass. Williams hit a runner at the other end and later shouldered past Eddie House to hit a 10-footer with 4:41 left.
The Jazz were able to stretch a four-point lead out to 98-89 before the Celtics called timeout with 3:51 left. Posey and Paul Pierce both missed three-pointers as Williams hit the shot against House and Carlos Boozer nailed a turnaround.
The Celtics came up empty on five straight possessions in crunch time as Pierce charged into Kyle Korver, Rajon Rondo airballed a drive, and Rondo was called for an offensive foul against Williams.
Williams sank both free throws after the Perkins flagrant foul and yelled after hitting a three-pointer with 2:06. The loss was the biggest of the year for the Celtics, who own the NBA's best record at 51-13.
After surrendering 62 points in the first half, the Celtics toughened in the second half, double-teaming Williams off the pick-and-roll and collapsing on Boozer. Kevin Garnett came alive in scoring eight points and the Celtics gave up just 17 in the third quarter.
That included a prayer of a three-pointer tossed in by Andrei Kirilenko to beat the shot clock. Jazz coach Jerry Sloan was whistled for a technical foul without even getting out of his seat and the Celtics got as close as four after a Garnett layup.
The Jazz were locked in from the start and ended the first quarter with a 33-23. Boozer scored 10 points in the quarter, leaving Perkins in his dust on a drive to the basket and splitting two defenders for a layup after grabbing an offensive rebound.
There also were early signs things went entirely right with the Celtics. Garnett missed his first four shots and had a ball poked out of his hands by Boozer. Rondo grew animated during a timeout with 7:40 left in the first quarter.
Ray Allen played the entire quarter but left for the locker room with a jammed left ankle. Allen didn't return the rest of the night, Garnett missed two free throws in the second quarter and Pierce went to the bench with his third foul with 3:51 left in the half.
The Jazz shot 58 percent in the first half and were able to built a 14-point lead as Okur hit a three-pointer and Boozer rolled down the lane for a layup as part of a three-point play. Williams sank two free throws to send the Jazz into halftime with a 62-49 lead.