The 76ers (38-37) snapped a two-game losing streak and pulled within a half-game of idle Washington and Toronto in the three-way fight for playoff positions 5-7 in the Eastern Conference.
The Nets' third straight loss dropped them 3½ games behind Atlanta for the final playoff spot in the conference. New Jersey (31-44) is down three games in the loss column with seven left in the regular season. The Nets are now 10th in the East, trailing Indiana by a half-game.
Vince Carter had 29 points to lead New Jersey, while Devin Harris added 22 and Richard Jefferson had 14, but just one in the second half.
Down by five entering the fourth quarter, the Nets cut it to 93-91 on Carter's 3-pointer from the left corner with 4:11 to go.
Williams then took over. He nailed a 3-pointer from the corner off Iguodala's feed on the 76ers' next possession for a 96-91 lead.
After Josh Boone scored on a rebound for New Jersey, Williams sandwiched a reverse layup and a jumper around a missed 3-pointer by New Jersey's Bostjan Nachbar for a 100-93 lead with 2:28 to play.
Iguodala stole the ball from Carter on the next possession and Dalembert scored inside for a 102-93 lead.
New Jersey never got close again as its magic number for missing the playoffs for the first time in seven years fell to five. That's any combination of Hawks' wins and Nets' losses.