Stoudemire had 28 points and 11 rebounds, and Phoenix beat Memphis 127-113 on Tuesday night as O'Neal sat out with a right hip contusion.
O'Neal, injured Sunday in a loss to Dallas, is expected back for Wednesday's game at San Antonio.
Stoudemire shot 10-of-13 from the field as the Suns won their eighth straight over the Grizzlies and moved a half-game behind the idle Houston Rockets for the fifth spot in the Western Conference playoffs.
"This would have been a big loss if we lose it," said Suns guard Steve Nash, who had 16 points and eight assists. "We really have to be professional and get a win even though it didn't have a lot of playoff atmosphere."
It was a typical Stoudemire night against the Grizzlies. In three games this season, Stoudemire is averaging 27.3 points against Memphis, while shooting 76.7 percent from the field.
"We wanted to win it from the inside, and, without Shaq, we were undermanned in the interior," Stoudemire said. "I just tried to attack in many ways. Just try to keep them off-balance a little bit."
Rudy Gay matched his career high with 36 points for Memphis. Mike Conley finished with 19 points and five assists before fouling out in the closing minute, and Kyle Lowry had 13 points off the Memphis bench.
Stoudemire's dominance in the middle was complemented in the second half with the outside shooting of Bell, Barbosa and Giricek. Memphis never really threatened after Phoenix built the lead to double digits in the third period.
Gay made it a bit interesting with 16 points in the fourth quarter, hitting a 3-pointer with 2:34 left to pull Memphis within 114-106. But a 3-pointer by Nash put Phoenix back ahead by double digits.
"He can make shots and you can't turn that off," Phoenix coach Mike D'Antoni said. "We talked about that, to get enough cushion that if he made some 3s, we could still win."
Both teams shot well in the game, Phoenix hitting 57 percent, the Grizzlies 56 percent. The Suns also made all 21 of their free throws.
Phoenix led 54-48 at the break, benefiting from 10 Memphis turnovers.
"We got into our kind of game, up and down," Conley said. "We know they like to play that style, so we knew it was going to be a good game for us offensively."
Unfortunately for the Grizzlies, they were playing against the team where coach Marc Iavaroni learned the style. Iavaroni was a Suns assistant before taking over the Memphis job this season. And, even with O'Neal out, the Suns still were able to dominate.
"The problem is that this is one of the best offenses in the league," Iavaroni said, "and they have so many weapons. Not only on defense, but on both ends of the floor."
Stoudemire had 14 points, connecting on 5-of-8 before intermission.
Memphis, which missed its first five shots, managed to stay with the Suns early by hitting 13 of its next 19 shots after the slow start.
But the 10 miscues contributed to 17 first-half points for the Suns. Phoenix closed the half outscoring Memphis 12-4.
After the break, Memphis still couldn't handle Stoudemire, as the Suns center got free for a trio of dunks before the midway point of the period. That was part of his 11 points in the quarter. Bell, who had 12 in the stanza, started connecting from outside, and his 20-footer gave Phoenix its first double-digit lead, 70-59, which the Suns extended to 89-75 entering the fourth quarter.
"We were able to get things going and make some open shots," Stoudemire said. "That opened up the court for us."
With O'Neal sitting down, Stoudemire moved over to the center spot in the Suns' lineup and Diaw started his 19th game of the season. ...The Grizzlies have surrendered 100 points in their last 11 games. ... Memphis, which was coming off a 113-101 victory at Minnesota on Sunday, has won consecutive games only twice this season. ...One of the biggest ovations of the night came in the second quarter when the Grizzlies congratulated the Memphis Tigers on their season that ended Monday night in a 75-68 overtime loss to Kansas in the NCAA championship game. ... Gay has scored at least 20 points in the last seven games. ... Grizzlies G Javaris Crittenton was out with a sprained right thumb he suffered in Sunday's game at Minnesota. He officially is listed as day-to-day. ... Stoudemire recorded his 36th double-double of the season.