Terry Rozier, starting in place of injured Kyrie Irving, added 23 points, Marcus Morris scored 21 off the bench while Jaylen Brown netted 20 and Jayson Tatum contributed 19 points and 10 rebounds for the Celtics.
“We’ve been down a lot, a lot of injuries, and we’ve always found a way,” Horford said. “Morris made some big shots, Tatum down the stretch, Terry — that’s what we’re all about. We just find a way.”
Greek star Giannis Antetokounmpo led the Bucks with 35 points, 13 rebounds and seven assists and gave the Celtics headaches until fouling out in overtime.
“He’s a great player,” Horford said. “He knows how to finish around the rim. He has great touch. We tried to contain him as best we could. We made a lot of turnovers. We have to work on that. I’m just glad we got this first win.”
Khris Middleton added 31 points, hitting 5-of-7 3-pointers, with eight rebounds and six assists in a losing cause.
The Bucks, who have not won an NBA playoff series since 2001, have been losers in seven consecutive first-round playoff series.
Rookie Tatum made his playoff debut with some key shots, including a back-to-the-basket layup scooped over his right shoulder for a 108-105 Boston lead and the Celtics made their free throws down the stretch to seal the victory.
Malcolm Brogdon’s 3-pointer had lifted the Bucks level at 96-96 with 10.3 seconds remaining. Rozier, making his first playoff start, sank a 3-pointer with a half-second remaining to give Boston the lead but Middleton drilled another equalizer from halfway between the arc and half-court at the final buzzer to force over-time at 99-99.
Boston closed the first quarter with a 15-0 run for a 29-17 lead but the Bucks answered with a 15-2 run for a 32-31 lead, Antetokounmpo’s 3-point play closing a 10-0 Bucks run to seize the lead.