James had a triple double in a losing cause with 24 points, 10 rebounds and 12 assists.
Tatum brought the crowd to its feet early in the first quarter when he took an outlet pass from Horford and went in for fast break dunk over the outstretched arm of Antetokounmpo.
Rozier said he knows he's under a spotlight this postseason with Kyrie Irving out for the season following his recent knee surgery. "I know I gotta fill big shoes". "I'm glad that I was able to go in and finish the game".
Game 2 of the series is Tuesday in Boston.
Giannis Antetokounmpo showed out for the Bucks with 35 points, 13 rebounds and seven assists, with Middleton finishing with 31 points. The rest of Cleveland's starters only managed 25 points, Kevin Love with 17 rebounds but only nine points. Brogdon scored all 16 of his points after halftime.
"It's forcing our group to grow up quicker than maybe some of our guys were supposed to", forward Al Horford said. "It's all about winning", Antetokounmpo said.
Nobody thought the game would end in any other way.
The Celtics have proven they have enough shooters, and they do not need any one player to be hitting 30 points on a nightly basis for their offense to be good.
Syria says Western attack 'doomed to fail'
According to USA officials, the operation comprised three United States destroyers, a French frigate and a U.S. submarine. She says the USA was confident that they had "significantly degraded his ability to use chemical weapons ever again".
Towards the end of the fourth quarter, Boston had a two-point lead until rookie Jayson Tatum made a rookie mistake which resulted in a turnover. He made two free throws to put the Celtics in front 110-106 with 18.8 remaining. The game had to be over at that point, right?
Rozier added three free throws to provide the final margin.
Each team had advantages and their fair share of weaknesses throughout the game-the Bucks had 20 turnovers which converted into 27 points for the Celtics while Milwaukee came out, guns blazing in the second quarter as they topped the Celtics in scoring on a 26-7 run.
The Milwaukee Bucks shot 48.2 percent from the field while the Celtics shot 41.5 percent, and they still lost.
Morris then knocked down a wicked filthy step-back jumper to put the C's up, 91-87, with 1:45 left. But Horford was steady again after being fouled, connecting on two more from the line with 15.2 seconds left.
Out of a timeout, Brogdon got free on the wing and drained a three with 10.3 to play to tie it at 96. Tatum then came down with another defensive rebound on the second missed free throw on a play in which Eric Bledsoe fouled out of the game.
But after a Milwaukee timeout advanced the ball to half court, Middleton matched it with his own 3 over Jaylen Brown as time expired.
"I think understanding the tendencies, understanding your roles, understanding assignments, all of those things become paramount because each possession is important", Bucks coach Joe Prunty said.