In regulation, Rondo's long jumper from the right wing gave Boston an 86-84 edge, but Boozer hit one free throw after being fouled by Pierce on a baseline drive with 23 seconds left.
Garnett then nailed two free throws with 20.1 seconds remaining and Hinrich hit one, cutting it to 88-86.
The Bulls forced the jump ball on the defensive end with 9.4 seconds left and gained possession before tying it on Hinrich's jumper.
Garnett airballed a long fadeaway as the horn sounded, sending the game to OT.
"We talked about it — you knew they were going to trap," Boston coach Doc Rivers said, "and you've got to do whatever you can do not to get tied up."
Rondo scored five points in Boston's 6-0 run, giving the Celtics their first lead at 80-79 with 4½ minutes to go.
Hamilton's layup gave the Bulls an 81-80 edge on the next possession before the teams started to trade trips to the foul line that led to pair of ties over the next 3 minutes, the last before the end of regulation when Garnett made one of two free throws to tie it at 84 with 2:20 left.
The Celtics tied it again at 79 on Rondo's two free throws a little over a minute later.
Bulls forward Luol Deng appeared to aggravate his sore right hamstring, injured in Wednesday's win at Toronto, when he came up limping after a fast-break drive to the basket late in the third quarter. He left the game for a substitute when play stopped.
After the game, Deng said he wasn't sure if he could play Saturday.
"It's pretty swollen," he said.
Boston guard Avery Bradley missed the game with a rib injury sustained in Wednesday's loss to New Orleans.
Noah had his double-double after three quarters, collecting 12 points and 10 boards. Boozer had 17 points and 15 rebounds after three.
Rondo had a highlight three-point play late in the third quarter that cut the Bulls' lead to 62-59. He was dribbling to the right of the lane when he lost his balance, falling to the floor, but kept his dribble going before getting up and driving in for a basket and a foul.
NOTES: Chicago G Derrick Rose, expected back in late February from knee surgery, participated in the team's shootaround. Deng didn't take part, but started the game. ... The Bulls play the first of four straight at home Saturday against Memphis. ... Rivers and his former assistant, Bulls coach Tom Thibodeau, had dinner Thursday night to celebrate Thibodeau's 55th birthday. "We went to dinner last night and the first thing I told him was, 'By the way, your team is pretty good without Derrick, that's No. 1,'" Rivers said. ... Garnett and Noah were each given a technical late in the fourth.