"I mean that's what great players do. I would love to tell you I had something to do with it," Celtics coach Doc Rivers said. "I was sitting just like the fans saying, 'Please, Lord, Paul make a shot.' "
Terry, who had missed five consecutive 3-point shots in the first two overtimes, also made the defensive play of the game when he stole the ball from Andre Miller with 35 seconds remaining.
Denver had one last gasp as Miller missed a 3-pointer with 4.9 seconds remaining before Terry dribbled the ball up the court and made a layup at the buzzer to finish the scoring.
"We're not into moral victories, but it was one of those games," Miller said. "It was a fun game, and I'm sure everybody was tired."
Denver's Lawson had 29 points, nine assists and six rebounds and hit several key shots, including a running bank shot to send the game into overtime tied at 92-92.
Gallinari struggled from the field, shooting 7 of 20. Kenneth Faried had 14 points and 12 rebounds for Denver.
Garnett was 3 of 4 from the field in overtime after missing 14 of his previous 20 shots.
With Denver leading 105-104 in the second overtime, Lawson hit another jumper to put the Nuggets up 107-104 with 18.9 seconds remaining.
But Pierce hit a 3-pointer with Miller in his face with 5 seconds left to tie the game at 107-107.
Gallinari then had an open lane to the basket as he was overplayed by Garnett, but missed his shot as time ran out.
Jeff Green's 3-pointer tied the game at 99-99 with 23.8 seconds remaining in the first overtime, but Lawson's long 3-pointer fell short at the buzzer.
"Lot of people still doubt us," Green said. "Can't come into games thinking we have to impress people."
Denver failed to hit its last shot in all three overtimes with chances to win the game in the first two and to tie it in the third.
Green's jumper put Boston ahead 92-90 with 47.9 seconds remaining in regulation. Miller then missed consecutive shots on the ensuing Denver possessions, but Faried was fouled with 5.4 seconds remaining.
Faried missed both free throws, but Celtics guard Avery Bradley knocked the ball out of bounds. Lawson then scored with 0.8 seconds remaining.
Gallinari, who averages 20 points per game to lead Denver, was held to three points in the first half on 1-of-6 shooting as the Nuggets trailed 50-46 at the break.
Pierce and Lawson each played 54 minutes respectively. ... JaVale McGee had 16 rebounds for Denver. ... Boston is 13-2 in its past 15 home games against Denver, but the teams are 10-10 head-to-head in the past 20. ... Boston matches up again on the road with Denver on Feb. 19. ... This had been the Nuggets' longest winning streak since March 30 to April 15, 2005. ... Andre Iguodala left the game for Denver in the third quarter with a strain and did not return.
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BOSTON, MA - FEBRUARY 10: Avery Bradley #0 of the Boston Celtics warms up before playing against the Denver...
The Celtics' triple-overtime victory Sunday was fueled by a pair of clutch shots. Jeff Green hit a game-tying 3-pointer with 23 seconds remaining in the first overtime and Paul Pierce hit a game-tying 3-pointer with 5 seconds remaining in the second overtime.
Entering the game, the Celtics had hit three game-tying or go-ahead shots in the final 24 seconds of the fourth quarter or overtime this season (3-of-22), only one of which was a 3-pointer (1-of-10).