Thomas knocked down six 3-pointers and went 11 for 21 from the floor. Boston made 14 of 40 attempts from distance and shot only 41.6 percent from the field.
Milwaukee got 21 points from Giannis Antetokounmpo and 17 from reserve Michael Beasley. But Jabari Parker started 0-for-8 from the floor and went 2 for 13 from the game to finish with four points while the Bucks shot 42.5 percent.
Milwaukee trailed by 11 at the half but Thon Maker used a dunk and layup on consecutive possessions to cut the deficit to five with 7:53 left in the quarter, part of an 11-0 Milwaukee run.
But while Boston went 7 for 21 from the floor, Thomas scored six in the quarter and went into the fourth holding an 81-73 lead.
The Bucks stormed back and cut the deficit to one when Monroe fed Antetokounmpo for a reverse layup to make it 88-87 with 7:31 remaining.
Antetokounmpo’s 3-pointer tied the game at 90 with 6:30 to play and a three-point play from Greg Monroe with 4:54 left gave Milwaukee a 95-94 lead — its first of the game.
The Celtics responded with five straight but Milwaukee tied it up again at 102 when Monroe hit one of two free throws with 36 seconds remaining in regulation. Both teams had chances to win it in the closing seconds, but couldn’t cash in.
After Boston scored the first six points of overtime, back-to-back 3-pointers by Snell tied things up at 108 with 1:13 left.
He got one more chance, with 45 seconds to go, but came up short and Crowder hit four free throws over the final half-minute to close it out for Boston.
NOTES: Boston C Al Horford was expected to return Saturday night after sitting out Friday with a strained groin, but instead did not travel to Milwaukee and sat out a second straight game. The Celtics were also without G Avery Bradley, who missed his sixth straight game with a sore right Achilles. … Bucks rookie F Thon Maker was in the starting lineup for the second time in his career Saturday. Maker scored a career-high eight points in eight minutes Friday night at Toronto. “We would like to see more (from Maker), so somebody has got to sit and we’re going to start him tonight,” Bucks coach Jason Kidd said before the game. … The Bucks and Celtics were meeting for the first time this season. Boston won the season series a year ago, taking three of the four games, but the teams split their previous six meetings in Milwaukee.