"I was brought here to make big shots and make plays and be a spark off the bench," Terry said.
Terry, Jeff Green and Paul Pierce all hit 3-pointers in the OT, and the Celtics held the Hawks without a field goal over the final 2:14.
Pierce finished with 27 points, seven rebounds and seven assists. Kevin Garnett had 17 points and eight rebounds and Terry scored 19, 11 more than Atlanta's reserves combined.
"Jason really stepped up. We count on him late in games," Pierce said. "Even if he doesn't get the shot, he's such a threat late in games that you can't come off of him. He's hit so many big shots throughout his career. He understands the moment and that's why he's here."
Boston won its fifth straight and is tied with the Hawks at 34-27, sixth in the Eastern Conference.
"We just continue to fight. In the stretch run of the season, every game is crucial," Pierce said. "Between the fourth and eight spot, it's a difference between 1 or 2 games so all these games are big and we understand the sense of urgency."
The Celtics improved to 7-4 in overtime and set a franchise record with their 11th OT game this season.
Josh Smith scored 32 points and Jeff Teague had 26 points and nine assists for the Hawks, who outscored the Celtics 48-32 in the paint but couldn't overcome a pair of turnovers by Smith in the final minute of OT.
"I had a couple of turnovers that I wish I could've had back," Smith said. "We couldn't come up with the big rebound that we needed in that overtime."
Al Horford added 22 points and Devin Harris scored 12 for Atlanta. Four starters scored in double figures for the Hawks, but only two other players scored at all for Atlanta in its fourth loss in five games.
The Hawks did make it a thrilling finish in a game Boston appeared to have in hand after a 10-0 run early in the fourth quarter. Atlanta still had time and didn't panic, using a 13-4 run to get back in it and force overtime.
Kyle Korver's 3-pointer with 1:31 left tied it at 92-all and was just the second field goal by a reserve for the Hawks. Pierce answered with a jumper, then Smith set up Horford on an alley-oop dunk to tie it up again.
"We just really wanted to make sure we controlled the rhythm of the game. I thought we did a good job for the most part of that late, particularly in the overtime," Atlanta coach Larry Drew said. "We just had too many bad plays on both ends of the floor."
The Hawks led 98-96 in overtime when Green got lucky for the Celtics with a 3-pointer that bounced high off the rim initially, but somehow stayed on target and went in after two more fortunate bounces and the Celtics had their first lead of overtime at 99-98. Smith answered right away with a 3-pointer, which Pierce matched with 1:37 left to put the Celtics ahead 102-101.
It was tied at 102 when Terry continued the 3-point frenzy on a 25-footer with 35 seconds remaining off a pass from Pierce.
Atlanta turned it over on a bad pass by Smith and Terry drew a foul, sealing the game with a pair of free throws.
The Hawks were on the road for the seventh time in eight games. ... Pierce scored 11 in the first quarter as the Celtics opened the game 11 for 19 (58 percent). ... Terry's 3-pointer with four seconds left in the second quarter gave the Celtics a 52-47 halftime lead. ... Anthony Tolliver was the only Atlanta reserve to score in the first half, finishing with five points. ... New England Patriots tight end Rob Gronkowski sat courtside and received a standing ovation when he was shown on the overhead monitor early in the fourth quarter.
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BOSTON, MA - MARCH 8: Jeff Green #8 of the Boston Celtics drives to the basket in front of Kyle Korver #26 of the...