Williams provided seven assists and six steals and Paul Pierce sank four 3-pointers en route to 25 points as Brooklyn led from start-to-finish and snapped an 11-game losing streak.
The Nets posted their first victory over the Lakers since Nov. 25, 2007.
Overshadowing the win was the appearance of Brooklyn's Jason Collins, who entered the game 1:32 into the second quarter and made history by becoming the first openly gay active player in any of the four major North American team sports.
Collins, who was signed to a 10-day contract Sunday, played 10:37 minutes with no points and two rebounds.
He revealed his sexual orientation in an April article in Sports Illustrated.