The Pacers were able to pull away in the final 9 minutes of the half, thanks to a 15-4 run that erased Memphis' largest lead of the half.
The rally helped Indiana carry a 43-39 lead at halftime as both teams had key players struggling with their shooting. West was 4 of 10 for Indiana, but Memphis struggled through much more inaccuracy.
The Grizzlies front line of Gay, Marc Gasol and Randolph was a combined 4 of 20, helping Memphis shoot 39 percent in the half.
The Memphis bench did provide a bit of a lift with 18 points, eight of them from Ellington, who connected on a pair of 3-pointers.
Memphis used defense to get its offense untracked in the second half. Through the first 8 minutes, Indiana had taken only six shots and had six turnovers.
That allowed Memphis to score 14 straight points to retake the lead.
For the quarter, Indiana was 8 of 12 from the field, and the Pacers used a 3-pointer from Orlando Johnson late in the third to hold a 65-63 lead entering the fourth.
The game remained tight through the early stages of the fourth until consecutive baskets by Tyler Hansbrough and a rebound basket by Hibbert broke a 70-all tie, giving the Pacers a bit of a buffer near the 7-minute mark.
Indiana maintained the lead until a 3-pointer from Conley with 2:10 left gave Memphis a 79-78 lead.
George immediately answered with a 3-pointer for the Indiana lead at 81-79.
"That was a huge answer-back three," Pacers coach Frank Vogel said. ".That is competitive spirit rising up. That was a huge play."
Tony Allen's hustle was what pulled Memphis back even. He grabbed an offensive re bound with about 30 second left, then stole the ball from Hibbert after an Indiana rebound with 11.7 seconds remaining.
That set up his pass to Randolph to tie the game at 81 with 10.5 seconds left.
The Pacers, who are now 10-13 on the road and have struggled against top teams, relished the idea of starting a four-game road trip with a win over one of the top four teams in the Western Conference.
"Coming in here, knowing it was going to be a tough environment, it was important," Hill said of the win. "(The Grizzlies) play well at home, and we knew it was going to be a scrappy, playoff mentality-type game.
"We knew we had to turn things around," Hill said. "Coach challenged us to be above a .500 road team, and it started with (Monday)."
NOTES: The game was the 11th Annual Martin Luther King Day game hosted by the Grizzlies. Memphis is now 5-6 on the holiday. ... The Grizzlies honored former NBA players Elgin Baylor and Patrick Ewing, along with former NFL great Jim Brown with the Eighth Annual National Civil Rights Legacy Award, as part of the day's ceremonies.