He made a floater that gave Atlanta a 94-92 lead. Then he hit three-pointers on the Hawks' next two possessions to make it a 100-95 game with 1:12 left.
Williams, who signed with Atlanta in 2012, finished with 22 points off the bench. He scored 12 points above his season average.
"He went back to the old Lou today," Sixers power forward Thaddeus Young said. "He's been having a rough season, you know, [he] played well in spurts.
"When Lou was here . . . he was able to do the same thing: light it up really quick and be able to come off the bench and be one of those main, key guys."
Williams' late-game heroics were aided by poor execution by the Sixers.
Rookie point guard Michael Carter-Williams committed a costly turnover with 2:45 remaining and the score tied. While the Sixers were overplaying Paul Millsap, Williams drained an open look from nine feet out.
"From that point forward, we were playing catch-up," Sixers coach Brett Brown said." I think [we're] just trying to take a young team and say, 'Here it is. It's tied at 92 and you're playing against a team that's scratching and clawing to try to get into the playoffs.' This is real basketball."
Millsap, an all-star power forward, finished with 28 points and 17 rebounds.
Young had 23 points and four steals to lead the Sixers. The power forward made 5 of 6 three-pointers. Shooting guard James Anderson added 19 points in the loss. Carter-Williams had 16 points, 9 rebounds and 9 assists.
This setback was the team's 27th in 28 games.
The Sixers have not won consecutive games since they took four straight against the Los Angeles Lakers, Denver Nuggets, Sacramento Kings, and Portland Trail Blazers from Dec. 29 to Jan. 4.
Despite its struggles, Atlanta (31-42) was supposed to put the Sixers back in their place. But Brown's team gave the Hawks a run for their money.
"Defensively in the second half, we were significantly better," Hawks coach Mike Budenholzer said. "I think it started in the second quarter. We held them to 22 [points] and got better."
It can be argued that the Sixers faced the previously reeling Hawks at the wrong time. That's because shooting guard Kyle Korver and swingman DeMarre Carroll were back in the lineup to help snap a six-game skid.
Korver missed the last six games with back spasms. Carroll was sidelined in Saturday's loss to the Washington Wizards with a stomach virus.
The two starters have been key pieces for the Hawks. Atlanta is 1-9 in games that Korver missed and 1-7 when Carroll does not play.
The duo was a no-show the first half, scoring two points on a combined 1-for-10 shooting. But Carroll and Korver got things going in the third quarter.
Carroll scored four points in his team's 9-0 run in the final 1:20 of the third to give the Hawks a 75-73 lead. He scored seven of his nine points in the quarter. Korver scored all 11 of his points after intermission.
But it was Williams who took over the game late.
"Millsap had such a great game and creates so much attention," Brown said. "Sometimes maybe we overacted a little bit and got into scramble mode. We had done a good job on Lou up until that point.
"Then Lou did what Lou does, and the game was pretty much determined at that stage."