The win may prove costly for the Pelicans after reserve forward Ryan Anderson was taken from the court on a stretcher after he collided with Boston's Gerald Wallace early in the fourth quarter. Both players went to the floor hard. Anderson had 13 points and seven boards before leaving.
The Celtics said a preliminary diagnosis indicated a "cervical stinger." He was taken to a local hospital to be evaluated.
"I can't really disclose that stuff," Pelicans coach Monty Williams said when asked about Anderson. "We are just praying for his health. He looked like he was OK. I was more worried about his mother. I know she's at home, a nervous wreck, so hopefully she hears this message and is cool with the fact that he's OK and in good hands."
New Orleans won for the fourth time in six games, but had lost six of its last seven on the road.
"We were praying for him, but at the same time we've got to win a game," said Davis, who grabbed a pair of clutch rebounds. "It's good that he's OK. We're praying for him."
The Celtics, who missed 22 of 26 shots from the field in the final quarter, lost for the sixth time in seven games.
"I thought we had really good looks for the most part, I really did," Boston coach Brad Stevens said. "I thought we were much more aggressive and, for whatever reason, we didn't make shots."
Anderson was on his back on the court for a few minutes, getting checked out by the team's trainer and a Celtics' team doctor. After about five minutes, a stretcher was brought out and both teams surrounded him on the court as he was put on a back brace before being wheeled off with 11:02 to play. Wallace stood at the foul line -- about 20 feet away -- nearly the entire time, biting a towel.
"I didn't even see him," Wallace said. "We collided. I didn't even know he was there. He said he was all right."
New Orleans then had to play its best late.
"We got some crucial rebounds and I think defensively we put them in some tough situations down the stretch and we were able to rebound," Brian Roberts said.
With the Pelicans clinging to a 91-90 lead, Evans scored on a driving basket, but Green hit two free throws for Boston with 35.2 seconds left.
The Celtics had a chance to grab the lead after Evans lost the ball out of bounds after his driving shot was deflected by Kris Humphries. But Bradley's drive down the middle tipped off the rim and, after a scramble, Davis grabbed the rebound.
Following a timeout, Roberts was fouled and hit two from the line with 7 seconds left, making it 95-92.
Sullinger's 3-point attempt caromed off the backboard and Davis grabbed the rebound just before the horn sounded.
Green's 3-pointer had given Boston an 86-83 lead with just under 5 minutes to play. After Davis' putback sliced it to one, Jordan Crawford, who missed 12 of his initial 13 shots, nailed a long jumper, making it 88-85 with 3 1/2 minutes left.
Boston, which trailed by six at the half, used an 8-0 run in less than a minute to take a 65-62 lead on Bradley's two free throws with 3 minutes left in the third.
But the Pelicans scored seven of the quarter's final nine points to grab a 73-72 edge at the break.
The Pelicans led 22-17 after one and had a 49-43 edge at the intermission.
The Celtics were delayed by the snowstorm that hit the area and didn't arrive in Boston until 1 p.m. after traveling back from Thursday's night's loss in Chicago. ... Sullinger has been bothered by a bruised left hand. "He's uncomfortable, but he wants to play," Stevens said. "Unless he gets hit, there's nothing really that's a long-term issue to him playing." ... Davis entered the game leading the league in blocks per game (3.2). ... New Orleans' guard Eric Gordon played his second straight after missing three with a bruised hip. He scored 12.