Garnett scored 16 points with 10 rebounds, and he also drew an offensive foul on Derrick Rose with Boston nursing a three-point lead in overtime. Ray Allen, who scored 25 points, followed with a dunk on an assist from Paul Pierce to make it a five-point game.
After Luol Deng tipped in Kyle Korver's airball, Chicago had a chance to cut it to one point when Noah tried to take off on a fast break. But Garnett ran him down and tipped the ball to Glen "Big Baby" Davis; he hit the foul shots to clinch it.
Noah had 26 points and 12 rebounds for Chicago.
Boston has won four in a row, and has not lost at home.
Deng scored 20 and Rose had 18 points and nine assists for Chicago, which lost its second straight game and fell to 0-2 on the road.
The Celtics led by as many as 16 points in the third, but Chicago cut it to six points late in the quarter and took the lead midway through the fourth when C.J. Watson hit a 3-pointer to give the Bulls an 82-81 lead. Boston opened a six point lead before Deng hit a 3-pointer with 2½ minutes left, then he hit another with 1:18 left in regulation to make it 96-96.
The Celtics had the ball with 35 seconds left and a chance to take the lead, but Paul Pierce overthrew Allen, and Keith Bogans outran Allen to the loose ball, diving to the floor and calling a timeout before he rolled out of bounds.
That gave Chicago the ball with 23.3 seconds left. Rose dribbled the clock down before trying to drive against Rondo, but the Celtics point guard went low and knocked the ball away; it bounced to Noah, but he couldn't gain control before the buzzer sounded.
The crowd gave a warm welcome to Bulls coach Tom Thibodeau, a Celtics assistant for three years — including when Boston won an NBA title in 2008. But the biggest cheer was for Brian Scalabrine, who spent five years in Boston and became a fan favorite as a bench player on the '08 champions.
In fact, a video of Scalabrine's scoring and Thibodeau's coaching from their Boston days got a louder reaction than the later one commemorating Paul Pierce's 20,000th point as a Celtics. The other Boston players applauded Pierce, who remained on the bench and nodded.
Chicago led 23-19 at the end of the first quarter, but the Celtics scored the first 12 points of the second, most of it with the second string on the floor. The starters came back on to score seven out of eight points to complete a 22-3 run that turned a four-point deficit into a 15-point lead.
The Bulls cut it to eight points early in the third quarter and it was four points early in the fourth. Ronnie Brewer hit a jumper with 7 minutes to play to make it 79-77.
Notes: The crowd gave a big cheer when the scoreboard showed the Miami Heat losing in the fourth quarter to the New Orleans Hornets. ... Davis has drew two more charging fouls in the first half, giving him 11 for the season. The Celtics had 13 as a team coming into the game, compared to five for opponents. ... Shaquille O'Neal did not play for the third straight game because of a bruised right knee. Coach Doc Rivers said O'Neal was questionable for the road trip to Oklahoma City, Dallas, Miami and Memphis. ... Semih Erden and Omer Asik, teammates on the Turkish national team, matched up in the low post in the first half.