Mike Dunleavy contributed 20 points while Tyler Hansbrough had 12 points and nine rebounds for the Pacers, who had dropped three straight and 10 of 13.
Jrue Holiday led the Sixers with 19 points and Elton Brand added 18. Marreese Speights and Evan Turner each had 14, while Jodie Meeks had 13, and Thaddeus Young and Lou Williams 12 apiece.
Andre Iguodala returned to the Philadelphia starting lineup after missing the previous seven games with tendinitis in his right Achilles', but he was largely ineffective and didn't seem to have the same explosiveness to the basket. Iguodala shot 0 for 6 and finished with one point, seven assists and four rebounds.
Collison snapped a tie game with a short jumper in the lane, pushing the Pacers to a 101-99 lead. After Williams missed a 3-pointer for Philadelphia, Hibbert extended the Pacers' advantage to 103-99 with an 8-foot jump hook as the shot clock expired and 1:24 was left in regulation.
The Sixers previously led 94-92 after Meeks connected on a long 3-pointer. Indiana came right back with five straight points - a 3-pointer by Granger and a jumper by Brandon Rush - to go ahead 97-94 with 3:28 remaining.
Holiday then tied the game again at 97 with a 3-pointer. There were many empty areas in the lower bowl of the arena thanks to a pending snowstorm which developed right before tip-off. But the estimated crowd of about 5,000 was treated to a game that featured numerous lead changes in the fourth quarter.
Dunleavy scored 15 points in the first quarter and had 18 by halftime as the Pacers built a 57-49 advantage. Indiana shot 52 percent from the field and led by eight despite not attempting one free throw.
Notes: Collison had eight assists at halftime for the Pacers. Sixers C Spencer Hawes was whistled for a technical foul with 10:43 left in the third. Holiday added eight assists and seven rebounds.