Henderson had a crucial steal late in the game and scored four points in the final minute to help the Bobcats end a three-game skid. Josh McRoberts added 12 points and 16 rebounds for Charlotte.
Damien Wilkins had 20 points and nine rebounds for the 76ers, who were dealt a big blow to their already thin playoff hopes. Philadelphia came in six games behind Milwaukee for the eighth and final playoff spot in the Eastern Conference with nine games left.
Jrue Holliday, the only player in the NBA averaging at least 18 points and eight assists, had a miserable shooting night, going 2 of 24 from the field with a key miss in the final minute.
Philadelphia led by 16 early in the second quarter but the Bobcats battled back to take the lead in the third behind the play of Walker and Henderson.
The Sixers seemed poised to make a run late when Evan Turner's lane jumper with 2:30 left in regulation tied the game at 80.
The Bobcats took the lead when Walker beat his man off the dribble and penetrated the lane, tossing an alley-oop to Josh McRoberts for a dunk.
Holiday answered by putting back his own shot to tie the game.
After a Charlotte turnover, Wilkins made one of two free throws to give the 76ers an 83-82 lead, but Henderson came alive with big plays on back-to-back possessions.
After knocking down a 15-foot jumper in traffic, he stole the ensuing inbound pass and drove the length of the court to put in an uncontested layup with 30 seconds left, putting Charlotte up by three.
Rather than go for a 3-pointer and try to tie it, Holiday drove to the left side and missed, and the Bobcats grabbed the rebound with 22 seconds left. Walker added two free throws for the final margin.
The Bobcats entered the game short-handed with three centers - Brendan Haywood, Byron Mullens and Gana Diop - and guards Ramon Sessions and Jeffery Taylor out with injuries.
NOTES: With only 10 healthy players, coach Mike Dunlap was forced to turn to seldom-used Tyrus Thomas and Reggie Williams off the bench more than usual. Williams scored 12 off the bench... Turner had 14 points for the 76ers, which shot 35 percent from the field. ... The Bobcats host the Heat on Friday night.