Winslow Townson / AP

Rasheed Wallace of the Pistons celebrates after scoring against the Celtics on Thursday. Wallace had 13 points and 10 rebounds.

Billups was limited to nine points in Game 1, his first action since straining his right hamstring early in Game 3 against Orlando in the second round.

He shed the tights he wore in the opener and came out aggressively, drawing a foul on the first possession and hitting two free throws. He added two free throws later in the first quarter when he appeared to create contact while attempting a 3-pointer by kicking the Celtics’ Eddie House in the groin.

“One thing I told Chaunce, you ain’t got to be overaggressive out there,” Hamilton said. “You can take your time and be the captain of our ship, and we’ll try to do a good job of helping you out.”

The Celtics missed their first six shots in the second quarter and didn’t make a field goal until James Posey’s 3-pointer with 7:03 left that tied it at 27. McDyess scored the next five points and the Pistons led the remainder of the half, opening a 50-43 lead at the break.

Allen was limited to 11 minutes in the first half because of foul trouble. He picked up his third with 8:41 to go and didn’t play again until coming in when the Celtics had the ball in the final seconds of the half.

Boston stormed out of the half with a 15-4 surge, featuring eight points from Allen in his best stretch in a while, to open a 58-54 lead. The Pistons steadied themselves with 3-pointers by Hamilton, Wallace and Billups to regain the lead, and Allen later had to return to the bench when he picked up his fourth and fifth fouls.

“It’s sometimes the basketball gods,” Rivers said. “Things are going well and then he picks up his fourth and fifth. I took the gamble on it and actually lost.”

Detroit went 4-of-5 from behind the arc in the quarter, with Wallace’s 3 with 7.1 seconds left sending the Pistons to the final period with a 78-69 lead.

Notes: After a review, the NBA upgraded a foul Hamilton committed on Garnett early in the fourth quarter of Game 1 to a flagrant foul, penalty one on Thursday. Hamilton appeared to throw an elbow at Garnett’s head while being picked. “It was instinct, it was flagrant. I can tell you that, we thought that at the time,” Rivers said before the game. “But again, Rip’s a good guy, great guy, and it’s an emotional game, that kind of stuff happens.” ... New England QB Tom Brady and girlfriend Giselle Bundchen watched from seats behind the baseline. ... Hamilton played in his 112th playoff game, tying Pistons president of basketball operations Joe Dumars for second on the franchise’s career list. He will tie Bill Laimbeer’s team mark in Game 3.

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