The teams battled back and forth for the first three quarters before the Pacers pulled away late in the fourth with a 13-4 run.
Oladipo sparked the surge with a 19-footer and by the time the run was over, the Pacers had boosted their lead to 94-86 with six minutes remaining. They took over after that.
Oladipo scored a team-high 25 points for the Pacers, who have won two in a row and four of five.
"Everybody contributed," Oladipo said. "It's a collective team thing. We had to do a great job of playing team defence, making them work. I think we did a great job of that tonight."
"We finally found our groove in the fourth and wore them down," Young said.
Kemba Walker finished with 23 points and three three-pointers to lead the Hornets, who have lost two straight games and four of six.
A Turner three-pointer started a 7-0 run that extended the lead to 103-89 with 2:46 left. That marked the biggest lead of the game for Indiana.
Charlotte eventually cut the deficit to single digits in the final minute of the contest that included 18 lead changes.
The Pacers' next game is Wednesday, when they host Memphis.
Irving scored 10 points in the fourth quarter and shot 11-of-17 from the field overall for the Celtics, who won their second game in their last seven.
- Rattles in winner -
Brown's three pointer from the left corner turned out to be the game-winning shot.
Denver had a chance to win in dramatic fashion at the end but Will Barton's long attempt from three-point range was late and wide.
"They put us in some tough spots and I thought our guys battled," said Boston coach Brad Stevens. "We missed some good opportunities on offence. But we found a way."
Nikola Jokic finished with 24 points and 11 rebounds. Barton scored 19, Gary Harris 15 and Jamal Murray 14.
Mason Plumlee had 16 points and eight rebounds before he left with a leg injury in the fourth.
The Celtics beat Denver for the second time this season, also winning 124-118 on December 13.
Elsewhere, Kent Bazemore scored 22 points, including a tiebreaking three-pointer with 2:09 remaining, and the Atlanta Hawks rallied after trailing by 11 in the third quarter to beat the Minnesota Timberwolves 105-100.