The Philadelphia 76ers, meanwhile, are simply playing out the string after being eliminated from postseason contention.
Williams and the Nets will try to take another step toward clinching fourth place on Tuesday night when they host the 76ers.
After a disappointing home loss to Chicago - the team directly trailing them in the East race - the Nets (44-32) bounced back with a key 105-96 victory over Charlotte on Saturday to move two games ahead of the Bulls, who lost at Detroit on Sunday, for the fourth seed.
The Nets, 23-15 at home, are hoping to build momentum heading into the postseason after dropping five of their last eight at the Barclays Center.
Williams has put together back-to-back outstanding performances there, finishing with 32 points on Saturday and making all six of his free-throw attempts in the final 1:16 to preserve the victory. He's totaled 62 points while shooting 20 for 34 from the floor and 18 for 21 from the foul line in his last two home games.
"This league is so full of big-time point guards. When you have one of, if not the best, it makes a huge difference,'' Nets interim coach P.J. Carlesimo said.
Williams has a chance to post three straight 30-point games for the first time since Dec. 10-13, 2010. He has averaged 21.7 points on 53.7 percent shooting in this season series, including 27 points and 13 assists in Brooklyn's only loss, 106-97 in Philadelphia on March 11.
The Nets took the first two meetings, 95-92 in Brooklyn on Dec. 23 and 109-89 in Philadelphia on Jan. 8.
The 76ers (31-45) had been playing well defensively, limiting opponents to 89.8 points per game and a 25.9 3-point percentage while winning four of five to keep their slim playoff hopes alive.
Philadelphia, however, allowed Miami to make 14 of 25 from beyond the arc in a 106-87 loss on Saturday. It was officially eliminated from the postseason that night when Milwaukee clinched the final spot with a win.
"I'm incredibly proud at how hard they've played every single night," coach Doug Collins said. "We've competed and we've had some really tough losses but we can only grow from that.''
Jrue Holiday - Philadelphia's leading scorer at 18.1 per game - has averaged 11.5 on 25.0 percent shooting (18 for 72) in his last four games and that was after scoring 18 on 7-of-17 shooting in Saturday's loss. He's averaged a team-best 19.3 points and hit all seven of his 3-point attempts in this series.
Evan Turner is also playing well, scoring 19.4 per game while shooting 53.5 percent from the floor in his last five.
The 76ers have made 23 of 50 (46.0 percent) from 3-point range versus the Nets, who have limited their opponents to 15 of 46 shooting (32.6) from beyond the arc in their last three overall.
Nets guard Joe Johnson had 15 points on 5-of-16 shooting in his second game back from a heel injury. He's averaged 19.0 points and hit 8 of 15 from 3-point range in this season series.
Brooklyn snapped a six-game home losing streak to the 76ers with its December win. The Nets haven't won this season series since sweeping four games in 2008-09.