The 76ers overcame a 38-point effort from Milwaukee's Caron Butler to snap a four-game losing streak.
Hawes converted a fall-away, 3-pointer -- his third in the final 1:21 of regulation -- with 1.7 seconds left to create a 102-102 tie. He then hit a layup that began a 7-2 run that finished off the extra period.
Evan Turner scored 27 for Philadelphia, which rallied from a 10-point deficit in the final three minutes of the fourth period. Hawes added 25 points, 11 of which came in the fourth quarter.
Butler made 13-of-22 shots and added eight rebounds. It was Milwaukee's seventh straight loss. The Bucks have won just twice this season, fewest victories in the Eastern Conference.