After Henderson gave the Bobcats an 85-84 lead with 3:58 remaining, Jason Terry made a 3 from the wing and Garnett followed with a turnaround jumper in the lane to push the Boston lead to four.
It appeared as though the Bobcats were on their way to another fourth quarter collapse.
But trailing by four, Henderson hit a 3-point with 1:01 left. After Bradley missed an open jumper, Sessions came free off a screen and knocked down an 18-footer to give the Bobcats the lead with 25.7 seconds remaining.
The Celtics called timeout but Garnett missed from the left wing. Mullens grabbed his 18th rebound and the Walker made a pair of key free throws to give the Bobcats a three-point lead with 14.8 seconds left.
Boston set up an inbounds play and Pierce got an open look but missed. He grabbed his own rebound and dished out to the wing for Bradley, but he missed a 3 as time expired.
Boston's loss came after a triple overtime win against Denver on Thursday night, but the Celtics refused to use fatigue as an excuse.
"We put that one behind us," Green said.
As he'd planned to do before the game, Rivers went deep into his bench in the first half with 10 players seeing at least 10 minutes of action.
The Bobcats battled back in the third quarter behind 12 points from Mullens to take a 75-72 lead into the fourth. Mullens, who scored Charlotte's first 10 points of the game, did most of his damage from outside, knocking down 3-pointers and turnaround jumpers, showing great touch for a big man.
"Byron was as good as you can get in the NBA statistically in many ways," Bobcats coach Mike Dunlap said. "He's still young. He's growing. ... He's a different player because he was able to take a res. He's got live legs and he's able to see the game."
NOTES: Pierce scored in double figures for the 50th game this season. ... Bobcats center Bismack Biyombo was a force inside on the defensive end blocking four shots and grabbing seven defensive rebounds.