On the ensuing inbounds, Rudy Gay's 24-footer over Paul George banked in, but it came after the buzzer - a ruling confirmed by officials after a review - giving the Pacers their second straight win and ninth in the last 11.
David West scored 14 points for the Central Division-leading Pacers, while George finished with 12 points, 10 rebounds and nine assists. Roy Hibbert scored 10 for Indiana.
Wayne Ellington led the Grizzlies with 17 points on 7 of 9 shooting, including connecting on all three shots from outside the arc. Gay had 14 points, while Mike Conley and Zach Randolph scored 13 apiece. Gay had eight rebounds, while Randolph added seven boards.
The game featured 10 ties and 19 lead changes.
Hill was sent to the line when Conley fouled him on a drive. Hill hit the second free throw, giving the Pacers the final lead.
The Pacers blocked 11 shots — five by West and four by Hibbert — a testament to their interior defense.
But Indiana had trouble taking care of the ball, committing 20 turnovers, compared to 15 for the Grizzlies.
Other statistical categories from rebounds (35-34 Grizzlies) to 14 second-chance points apiece were further indications of the game's closeness.
The teams scrapped through a tightly-played first half that featured 15 lead changes and six ties.
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. Neither team had a player in double figures as several key players struggled shooting. West was 4 of 10 for Indiana, but Memphis suffered through much more inaccuracy.
The Grizzlies frontline 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 in the second quarter.
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 unanswered points to retake the lead.
For the quarter, Indiana 8 of 12 from the field, and the Pacers used a 3-pointer from Orlando Johnson late in the third to carry a 65-63 lead into final frame.
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.
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 after an Indiana rebound.
That set up his pass to Randolph to tie the game at 81 with 10.5 seconds remaining.
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. .The Grizzlies opened a four-game homestand with Monday's game, while the Pacers were playing their first of a four-game road trip. .The Pacers defeated Memphis 88-83 on New Year's Eve in Indy.