Afterward, before anyone asked a question, O'Neal praised Stoudemire.
"Amare Stoudemire is the best big man in the game right now -- period, bar none," O'Neal said. "I didn't know he was that good. But talking to him and watching him play, he's the best big man in the game at 25, and I mean that. I'm not just saying that to pump him up."
Stoudemire did most of his damage with Kevin Garnett guarding him.
"He's doing what great players do," teammate Grant Hill said. "It was happening before, but it's really happening now that Shaq has come. Amare has just been phenomenal at both ends. Defensively, offensively he's just bringing it. I hate to put it out there but he's playing MVP caliber basketball."
Stoudemire appreciates being moved from center to his natural power forward spot.
"It's helped me a lot," he said. "It's just allowed me to play basketball. I don't have to battle so much with the big guys and get in foul trouble, things like that. Tonight was a great step for us."
Steve Nash added 18 points, including a pair of late 3-pointers, and Hill had 14 points and 13 rebounds to record consecutive double-doubles for the first time since Dec. 2-4, 2002. O'Neal had just four points but 14 rebounds as the Suns dominated the boards 50-32.
It was a rough game, but with O'Neal around, the Suns are not softies anymore.
"He gives us a big presence," Nash said. "We're not the short, skinny guys anymore. It's nice to be on that end of the battle sometimes."
Garnett scored 19 points, Paul Pierce was 2-for-13 shooting for five points and Ray Allen scored 11 points and shot 3-for-12.
The Suns played most of the game without Leandro Barbosa, who got a cut above the right eye on a shot from Pierce with 4:36 left in the game. The cut required three stitches and Barbosa did not return.
Phoenix went 12:05 without a field goal in the first half and still had the lead, 27-26. Nash ended the drought with a layup that ignited a 16-2 outburst that gave the Suns a 43-28 lead when Raja Bell made one of two free throws 1:05 before the break. Boston's Rajon Rondo made a layup with 2.1 seconds to go to make it 43-30 at the half.
It was the fewest points in a half by Boston and the fewest by a Suns' opponent this season.
"I just think we were bad offensively," Celtics coach Doc Rivers said. "We have been very good offensively, tonight we were bad."
Boston trailed by as many as 16 in the third quarter. The Celtics cut it to nine early in the fourth quarter and seven in the final seconds.
Phoenix led by 13 at the break despite committing 15 turnovers in the game's first 17 minutes.
Garnett and Stoudemire were locked in a heated battle throughout. Garnett, in his third game back after missing eight with a strained abdominal muscle, drew his third foul with an elbow into Stoudemire and had to leave the game with 4:08 left in the half. Later, Stoudemire drew a technical for shoving Garnett.
The Suns committed 11 turnovers in the first quarter but still led 24-13 because the Celtics shot 21 percent (5-for-24). O'Neal was scoreless had four turnovers in the quarter.
Boston started 2-for-14 as Phoenix went on a 15-0 run to build a 19-4 lead on Barbosa's layup with 5:39 to play. The Celtics got back in it with a 10-0 surge to cut it to 27-26 on Garnett's dunk 7:50 before the break.
Boston's 13 in the first were the fewest points allowed by Phoenix in a quarter this season. ... Phoenix outrebounded the Celtics 18-4 in the first quarter. ... The Suns are home against Detroit on Sunday. ... Boston has Portland and the Los Angeles Clippers remaining on its trip.