Hill also nailed a key free throw with 14.1 seconds left in the fourth quarter to give the Pacers a 78-75 lead.
Earlier Roy Hibbert made one of his two free throws with 32 seconds left to put the Pacers up 77-75.
Players stepped up for the Pacers when it counted the most but West wasn’t reading too much into their first win in the best-of-seven series.
“We can’t celebrate over this,” West said. “We didn’t want to win just one game. We want to win the series.”
LeBron James finished with 28 points and Dwyane Wade scored 24 for the shorthanded Heat, who shot just 34.6 percent from the floor.
Wade had a chance to tie the game with 16 seconds left after Hibbert made one of his free throws but Wade spun around Hill to the left and missed on the layup attempt.
“We maintained our composure and got them off some of the things they like to do,” West said of the Heat.
A three-point try from Miami’s Mario Chalmers bounced off the rim at the buzzer as the Heat saw their playoff win streak at home against Eastern Conference opponents snapped at 13.
The second-seeded Heat defeated the Knicks in five games to advance to the second round.
The Heat captured the opener on Sunday with a 95-86 win, but lost star forward Chris Bosh to a lower abdominal strain.
Miami will likely not have Bosh back for the rest of the Eastern Conference series.
Game three of the series will be in Indianapolis on Thursday.
West said the Pacers need to come out strong in the opening quarter Thursday and play the same way down the stretch in order to win at home.
“We are going to remain aggressive, play team ball and put pressure on them to beat us,” he said.
Meanwhile, Chicago Bulls guard Derrick Rose, the 2011 NBA Most Valuable Player, could be out between eight and 12 months following knee surgery to repair a torn anterior cruciate ligament, the NBA team said.
Bulls team doctor Brian Cole said Tuesday that Rose’s rehabilitation will involve a series of progressive steps.
“It’s really a series of progressions, very knee focused initially, which is what we’re doing now. We spread out from there, doing entire body conditioning, performance training and so forth.”
Rose could miss part of the 2012-13 season if the rehab takes as long as Cole indicated it might.
Rose suffered the injury in the first playoff game against the Philadelphia 76ers on April 28.
Chicago won the game, but went on to lose the series as the Sixers upset the top seeded Bulls. He underwent surgery on Saturday.