Reserve Mickey Johnson score 21 points, nine in the fourth quarter, and Darryl Dawkins had 10 of his 18 points in the final six minutes to lead New Jersey at home.
It was the fifth straight victory for New Jersey (17-13), which has won 11 of 15. Dallas (12-17) lost its fourth straight and eight of nine.
Albert King, New Jersey's starting small forward, suffered sprained ligaments in his right knee in the final second of the first half. King, second on the team in scoring, rebounding and assists, is expected to be out for two to four weeks.
Dawkins scored 10 points in a 3:49 stretch in the fourth quarter before fouling out with 2:10 remaining. He made two free throws and a 15-foot jump shot to give the Nets a 107-98 lead with 2:20 remaining.
Johnson and Dawkins scored 23 of the Nets' 29 points during a stretch between the third and fourth quarters. Johnson scored 15 points in the second half and converted nine of nine foul shots in the game.
Williams had 17 points and 12 rebounds. Mark Aguirre scored 25 points to lead the Mavericks and Jay Vincent had 23.