After coming up just short in a riveting overtime contest to open the series on Wednesday, the Pacers made the clutch plays down the stretch Friday to overcome a four-point deficit midway through a tense fourth quarter.
With Indiana having earned a road victory over the defending NBA champions and having defeated them twice in their three regular-season meetings, the Pacers will try to take command when the series moves to Indianapolis.
The Pacers will host the next two games on Sunday and Tuesday.
LeBron James delivered a 36-point effort to give the Heat a tremendous chance to grab the win, but he made two glaring errors when he turned the ball over twice in the closing moments.
Chris Bosh hit a 3-pointer for Miami to put the Heat in front 88-84 with 6:09 to play, but Indiana closed the contest on a 13-5 run.
Bosh converted two foul shots with 1:44 remaining that lifted Miami into a tie and they turned out to be the final Heat points.
Hill's two free throws with 48.9 seconds remaining put Indiana in front for good and James then made the two poor passes that decided the game.
His first turnover was picked off by West, but Indiana allowed the shot clock to run out without getting off a shot.
That gave Miami a chance to tie it or perhaps win it with a 3-pointer, but James again made a bad pass that was eventually collected by Hill.
Hill was immediately fouled and his two free throws with 8.3 seconds to go all but clinched the victory. That outcome was assured when Bosh missed a 3-pointer with 2.6 seconds left.
Indiana countered the performance by James with 29 points and 10 rebounds from Roy Hibbert, who made 10-of-15 from the field. George added 22 points and contributed 18.
Indiana shot 50 percent from the field and hit eight more free throws than did the Heat.