The Hawks, clinging to the final playoff spot in the East, snapped a six-game losing streak and won for only the seventh time in 27 games. They came into the night one game ahead of the New York Knicks.
Williams hit two crucial 3-pointers in the closing minutes as the Hawks bounced back from an early 14-point deficit.
The 76ers were coming off a victory over Detroit, snapping an NBA record-tying streak of 26 consecutive losses. But they couldn't win two in a row for the first time since Jan. 4.
Millsap carried the Hawks much of the night, also snagging a season-high 17 rebounds. But Williams hit the biggest shots down the stretch, back-to-back 3s from deep in the same corner, finishing off the 76ers.
Thaddeus Young led Philadelphia with 23 points, while James Anderson chipped in with 19.
The 76ers led from the opening minutes until late in the third, when the Hawks stormed to the front by closing the period on a 9-0 run. Williams got it going with a three-point play, DeMarre Carroll dunked off a turnover, Williams made two more free throws, and Carroll laid one in to give Atlanta a 75-73 lead heading to the final quarter.
Philadelphia turned it over twice and missed its final four shots of the period, the last of those a reverse layup by Elliot Williams that rolled off the rim. Atlanta's Mike Scott stood defiantly over Williams after playing him tough, the 76ers player sprawled out beneath him on the floor.
The Hawks shot just 32 percent in the first half, were out front for a total on only 29 seconds, and trailed 53-43 at the break.
NOTES: 76ers F Arnett Moultrie was suspended five games without pay for a league drug violation. Moultrie, who played 12 games for Philadelphia this season, was assigned to Delaware of the D-League. He can't play with the minor league team during his suspension, either. "Arnett is still a part of the team and we will reach out to him and help him where we can," coach Brett Brown said. ... Hawks G Kyle Korver had missed six games with back spasms before returning to the lineup. He had 11 points on 3-of-10 shooting. ... Atlanta swept the season series, following up a 113-103 victory at home and a 125-99 win in Philadelphia that started the 76ers' historic losing streak.