Instead, the Bucks have a 3-2 series lead.
Trailing by six points with 1:45 left in the fourth quarter, the Bucks won 110-107, securing the victory with two made free throws by Pat Connaughton with 5.9 seconds left in the fourth quarter.
Bobby Portis' offensive rebound and putback off a missed free throw by Giannis Antetokounmpo with 11.4 seconds left in the fourth quarter gave Milwaukee at 108-107 edge. It was Milwaukee's first lead since the second quarter.
Bucks guard Jrue Holiday came up with the defensive plays of the game, blocking a Marcus Smart shot with 6.6 seconds remaining and stealing the ball from Smart with one second left - before Boston could attempt a potential game-tying shot.
Game 6 is Friday on ESPN. The Bucks can close out the series and advance to the conference finals for the second consecutive season.
Here are three key takeaway from Game 5:
Giannis finds a way
Offense is not easy for Antetokounmpo against Boston. He's shooting well below his season averages from the field, on 3-pointers and on free throws against the Celtics. But he still makes an impact with his scoring and rebounding.
He had a game-high 40 points in one of his more efficient offensive games of the series: 16-for-27 from the field, 2-for-5 on 3s and 6-for-10 on free throws. He also had 11 rebounds, three assists, a block and a steal.
In the fourth quarter, he had eight points.
Getting help without Middleton
Khris Middleton's absence due to a sprained left knee was notable before the series began and glaring through five games. He is a 20-point-per-game scorer who can make 3s and mid-range shots, plus rebound, pass and defense. It's a significant loss.
There are times when the Bucks' offense sputters, and Boston's defense has something to do with that, too.
But Antetokounmpo had just enough offensive help even though he and Jrue Holiday (24 points) were the only starters in double figures.
Portis finished with 14 points, including six in the fourth quarter, and he collected 15 rebounds including that offensive rebound that turned into the winning shot. Connaughton had eight of his 13 points in the fourth quarter.
Holiday struggled at times offensively, too, but he keeps playing hard. His eight rebounds, eight assists, two blocks and one steal were necessary.
Brown, Tatum carry C's offense
Jaylen Brown scored 16 of his 26 points in the third quarter, maintaining some distance between the Celtics and Bucks. Brown also had eight rebounds, six assists and a block.
Tatum had an off game shooting (12-for-29 from the field and 2-for-11 on 3s) but still managed 34 points, including 12 in the fourth quarter. He added six rebounds, four assists, a steal and a block.
Oddly, Tatum and Brown were the only Celtics to reach the foul line, attempting all 15 of Boston's free throws.
The Celtics shot 51.2% from the field, yet lost. Milwaukee shot just 43.5% from the field but 44.8% on 3s, and the Bucks outscored the Celtics 20-13 in second-chance points and 16-13 on points off turnovers. Milwaukee also outrebounded Boston 49-36, including 17-5 on offensive boards.
Follow Jeff Zillgitt on Twitter @JeffZillgitt.
This article originally appeared on USA TODAY: Bucks edge Celtics in Game 5 thriller to take 3-2 series lead