This win lifted the Sixers' spirits heading into Saturday's battle against the Indiana Pacers at Bankers Life Fieldhouse.
"We were very lucky," said coach Brett Brown, whose Sixers won for just the third time in 11 games.
"At the end, Spencer [Hawes] got us where we needed to go," he added.
"Evan [Turner] grabbed the overtime . . . to make sure that we were not going to lose."
Turner scored eight of the Sixers' 13 points in the overtime session. His final basket, a jumper, gave them a 112-105 lead with 1 minute, 18 seconds left in the extra session.
The 6-foot-7 swingman moved to point guard after Michael Carter-Williams fouled out with 3.9 seconds left in regulation. He finished with a team-high 27 points to go with six rebounds and three assists.
"When Mike fouled out, [Brown] just came up to me and said 'Just take over the game,'" Turner said. "My teammates pretty much told me to lead us. That's what I tried to do."
Hawes added 25 points and made 3 of 6 three-pointers. All three of his threes came in the final 1:12 of regulation. The 7-foot-1 center's third one, a one-legged shot from the corner, knotted the score at 102-102 and forced overtime with 1.7 seconds left.
"Coach drew it up in the huddle," Hawes said of the corner-three play Brown got from former NBA coach Stan Van Gundy. "It reminded me of that last time a coach drew up a three for me to tie a game. I was in college. I thought he screwed something up. I was like, wrong guy coach."
"But on a serious note, we knew they were switching and we had to combat that."
Caron Butler led the Bucks with 38 points.
It appeared Milwaukee would win in regulation after Butler drained a three-pointer with 8.9 seconds left to put the Bucks up, 101-97. Turner responded with a driving layup to close gap to two with 4.9 left.
Then Luke Ridnour hit a foul shot to make it a 102-99 game a second later. Hawes went on to forced overtime moments later.
Sixers backup point guard Tony Wroten left the game in the third quarter with a lower-back strain. He's not expected to play against the Pacers. Reserve Hollis Thompson scored a career-high 16 points on 7 for 9 shooting from the field.