The win put the Pacers two games over .500 for the first time this season.
Hibbert suffered a deep thigh bruise.
But Indiana held the Pistons scoreless for 6:05 in the fourth quarter while also getting big efforts from reserve big men Hansbrough and Pendergraph. Hansbrough had 11 points and six rebounds in almost 25 minutes, and Pendergraph two points and three rebounds in just under eight minutes.
"Guys stepping up after we lost Roy to an injury," Pacers coach Frank Vogel said. "... Pendergraph and Hansbrough really stepped up."
Paul George added 15 points, eight rebounds and eight assists.
"It came down to a grind game in the last eight minutes of the game. They did what they do best and that's win grind games," Detroit rookie center Andre Drummond said. "They're a great team and David West hit a lot of tough shots today. It was a learning game for us today."
Kyle Singler's jumper brought Detroit within two at 68-66 with nine minutes left.
But that's when the Pacers defense put the clamps on the Pistons offense, which didn't score again until Stuckey's driving layup with 2:55 remaining.
"That's what we've been preaching all year long: The defense is going to get us the wins," Hill said.
West added: "We just try to make teams score through us or over us."
Indiana scored 11 points during that span.
West hit a free throw with 7:23 left, George put in a driving lay-in at 6:03, West hit a hook with 5:21 remaining, Hill hit a 3 with four minutes left, George made a free throw with 3:36 on the clock and West's turnaround jumper gave the Pacers a 79-66 lead with 3:17 left.
"Our crunch time defense has been solid for us this year," Vogel said. "And we've got big-time shot makers in George Hill and David West."
Detroit coach Lawrence Frank lamented the Pistons' dry spell.
"Really, you look right at the 8:23 mark, it was a two-point game," he said. "From that point on, we missed five jumpers, we had two turnovers and a missed layup."
Indiana took a 63-60 lead into the fourth quarter after Singler's 3-pointer with 1:29 left in the third and Drummond's put-back dunk with 49 seconds remaining in the quarter brought the Pistons to within three.
Indiana led 42-38 at the half.
The Pacers went on an early 15-0 run that gave them a 17-6 lead with 6:51 left in the first quarter after Gerald Green's 3-pointer.
But the Pistons followed that up with a 14-3 spurt that allowed them to tie the game at 20 on Stuckey's driving layup with 1:59 remaining in the opening quarter.
Vogel said he expected Hibbert to be ready for Indiana's next game, on Tuesday at Milwaukee. ... Pacers guard Lance Stephenson didn't play because of a sprained right ankle. ... Both teams were playing for the second consecutive night. The Pacers beat Philadelphia 95-85 at home and Detroit lost 107-105 in double-overtime to the Nets in Brooklyn.