Tatum added 10 rebounds and eight assists, Jaylen Brown scored 24 points and Al Horford made seven three-pointers on the way to 23 points.
But the shift came when the Celtics found a way to slow down Indiana's high-octane offence in the second half to snatch the win in Indianapolis, where they'll try to close out the series on Monday.
"Closeout games are the hardest," Tatum said, cautioning that the Celtics can't afford to relax despite the fact that no NBA team has rallied from 0-3 down to win a play-off series.
Pacers coach Rick Carlisle certainly wasn't ready to wave the white flag.
"We're going to be undeterred, we're going to be back here Monday night looking to extend the series and we're going to come at them even harder," vowed Carlisle, who said the Pacers played "a courageous game".
Indiana, who were unbeaten in six prior home games this post-season, came out determined to avoid the 0-3 hole despite the absence of All-Star guard Tyrese Haliburton, who aggravated the left hamstring strain that troubled him this season in Game 2.
Andrew Nembhard, taking over at point guard, scored 32 points and handed out nine assists and Pascal Siakam and Myles Turner scored 22 apiece for the Pacers, who pushed their lead to 18 in the second quarter and again in the third.
But a three-point play by Jrue Holiday, who was fouled on a driving layup and made the free throw, put the Celtics up 112-111 with 38.9 seconds to play.
It was their first lead since the first moments of the second quarter and they made it stand up, Holiday coming up with a decisive steal from Nembhard and making a pair of free throws to seal it.
"I think the and-one I just saw the opportunity," said Holiday, who was questionable to start because of illness until shortly before the game. "I think Siakam was on his heels so I just attacked him and got the and-one."
Despite the absence of Haliburton, the Pacers got their offence firing and erased an early nine-point deficit, exploding in the second quarter to build their first 18-point lead of the contest.
Another level
Nembhard scored 17 points in the second quarter and the Pacers connected on 15 of their 22 shot attempts to surge past the Celtics.
With 21 points by half-time Nembhard had already surpassed his career play-off high.
He drilled a long three-pointer with less than five seconds left in the first half to give the Pacers a 69-57 lead at the break.
Indiana were up by 18 again midway through the third, but Boston bore down defensively and reeled them in.
It remains to be seen if Haliburton will be available for Game 4 on Monday.
"It was determined that tonight was not an option," Pacers coach Rick Carlisle said before the game, saying Haliburton would be reassessed before Game 4.
Celtics coach Joe Mazzulla said the absence of Haliburton had left Boston struggling to adjust to early on.
"It took us a little while to figure out how we were going to match up with them in order to slow them down," he said. "I felt like it was our defence, and I thought we took it to another level in the second half."
