Rudy Gay scored 21 points for the Grizzlies as 92, at FedExForum on Friday.
The Grizzlies had five players in double figures, including 19 points and nine rebounds from Marreese Speights. Mike Conley and Marc Gasol each added 15 points apiece for Memphis, which has now won two straight after dropping its previous three.
"I know all the games aren't going to start off like that," Speights said about scoring seven of his team's first 11 points. "I just go out there with a little more energy and try to get on the boards early and start the momentum."
The two teams ended each quarter tied and the third was no different as another back-and-forth quarter found the game tied at 73.
Gay capped a 12-2 run with a three-point play after drawing contact on a dunk but Indiana quickly answered with a 9-0 run to pull the game even at 86 with 4 1/2 minutes to go.
Two Gasol free throws capped a 7-1 Grizzlies run down the stretch as they led 93-87 with just over a minute remaining.
Granger hit a three with 21.1 seconds left to put Indiana down just three, forcing the Grizzlies to earn the win at the free throw line.
O.J. Mayo calmly hit both free throws to give the home team a five-point edge with 19.2 ticks on the clock.
Paul George would air ball a three-point attempt on the next possession and Mayo knocked down his first, and pulled down the offensive rebound on his second to seal the victory for Memphis.
"The biggest difference was the willingness to win," said Pacers point guard Darren Collison. "They had a little bit more will than us. They wanted it more, and that's something we just can't have."
Gasol scored back-to-back buckets around a Jeff Foster tip-in as the first quarter finished with the two teams tied 22-22.
Gasol would again cap the scoring in the second as he made 1-of-2 from the charity stripe to pull the Grizzlies even, 46-46, at halftime.
Indiana has dropped five in a row to the Grizzlies...Indiana will host Denver on Saturday in the second game of a back-to-back, while Memphis will host Utah on Sunday...The Grizzlies shot 11.1 percent from long range and the Pacers finished at 37.5 percent...Memphis' Dante Cunningham was ejected in the third quarter after receiving two techinals for arguing two different calls.