The Nets won their third game in a row to remain in fourth place in the Eastern Conference with four games to play. Brooklyn (46-32) is three games behind the Indiana Pacers and 3½ ahead of the Chicago Bulls and Atlanta Hawks, in excellent position to secure home-court advantage for the first round of the playoffs.
Paul Pierce scored 23 points for Boston (40-38). The Celtics have lost nine of their past 13 yet still sit comfortably in seventh place in the East, three games in front of the Milwaukee Bucks with four to go.
Kevin Garnett chipped in 11 points and eight rebounds for Boston in just his second game back after missing eight due to left ankle inflammation. Jeff Green also scored 11, and Brandon Bass had 10.
Boston and Brooklyn hadn't met since the Celtics crushed the Nets by 17 on Christmas Day in a game featuring three ejections.
Wednesday's game was a one-sided fight.
The Nets - who hit 25 of 28 free throws - opened up a 13-point lead early in the fourth after four straight points by Kris Humphries, but Garnett converted a three-point play to trim the deficit to 10 with under nine minutes to go.
Boston crept within eight when Green delivered a three-point play, but the Celtics had no answer for Williams down the stretch.
The pesky point scored six straight points for Brooklyn, sinking a long jumper and then knifing through the lane for a layup that all but put the game away at 95-82 with 4:35 to play. Lopez later capped an 8-0 run with a dunk that made it 99-82.
On the heels of a game-altering spurt to the close the first half and open a double-digit lead at the break, the Nets picked up in the third quarter right where they left off.
Johnson hit a 3-pointer from the top of the arc, Williams sank a long jumper and Jerry Stackhouse added a baseline jumper that handed the Nets a 60-45 lead.
Pierce twice sliced the lead to 12, but Brooklyn ballooned the lead to 68-52 with 5:37 to play in the third behind six points from Lopez and another jumper from Stackhouse.
Boston whittled the deficit to eight following a 3-pointer from Green and three points from Pierce, but Brooklyn maintained its 10-point cushion entering the fourth.