The Lakers won their fourth in a row and recorded a victory on the road for the first time in four tries this season. Utah suffered its first home loss and had a five-game winning streak snapped.
The Lakers were clinging to a one-point lead with 51 seconds remaining in the extra period when Kobe Bryant, who finished with 40 points, missed a jumper. Bynum, however, was there with the tip-in to put Los Angeles in front 88-85.
Utah again closed within one on Millsap's jumper with 42 seconds left and the Jazz regained possession with a chance to take the lead. But Bynum blocked Jefferson's layup try and Bryant made two free throws with a second to play for the final margin.
Bryant blocked a desperation 3-point attempt to tie it at the buzzer by Devin Harris.
Bryant took 31 of the Lakers' 82 shots from the field and made 14 of them. He was 11-of-11 from the line.
Pau Gasol added 14 points and Bynum had 11.
Millsap led the Jazz with 29.