After watching Antonio Blakeney improbably rally the Bulls from a 105-101 deficit with a four-point play with 30.5 seconds to go on a foul by Collison, the Pacers called a timeout and got the game-winning shot from Collison 12 seconds later.
The Bulls had two subsequent chances to tie and a third to win, but Zach LaVine misfired on a 14-footer, Justin Holiday a 3-pointer with 5.7 seconds left and Blakeney a 19-foot buzzer-beater that was blocked by Myles Turner.
The win was the Pacers' fourth straight on the road and the fourth overall in their last five games.
Chicago, meanwhile, dropped a third straight in the midst of a four-game homestand.
The Bulls trailed 87-80 entering the fourth quarter, then got nine points from LaVine in a 19-5 period-opening run to pull into a 99-92 lead with 6:54 to go.
But the Pacers responded quickly with an 11-point burst to go up 103-99 on a jumper by Turner with 3:20 to go.
Indiana appeared to be in good shape until Blakeney hit his 3-pointer while being fouled by the eventual hero Collison.
Victor Oladipo recorded a game-high 25-point, 14-rebound double-double for the Pacers.
Turner had six blocks to complement 18 points for Indiana, while Collison added 14 points and Tyreke Evans 13 off the bench.
Blakeney had a team-high 22 points in a reserve role for the Bulls, who fell to 1-4 at home.
The Bulls ran out to a 33-17 lead in the first 10 minutes, then went up by as many as 18 early in the second period before the Pacers fought back.
Indiana used a 26-8 burst to pull into a 50-all tie en route to a 60-58 halftime advantage, then led 87-80 after three quarters.
(With inputs from agencies.)