Stoudemire had 31 points, including two game-clinching free throws with 7.5 seconds to play, and the Suns handed the Washington Wizards their seventh straight loss, 108-107 on Sunday night.
O'Neal has said he is making Stoudemire his special project.
Stoudemire seems to be doing just fine already.
"Amare is really good," Suns coach Mike D'Antoni said. "He's blocking shots, he's running, he's shooting -- and just his attitude. I can't say enough about him."
Stoudemire has consecutive games of at least 30 points and 10 rebounds for the first time since Feb. 8-9, 2005. In the three games since the big trade brought O'Neal from Miami for Shawn Marion and Marcus Banks, Stoudemire is averaging 30 points and 16.5 rebounds.
Stoudemire also had 13 rebounds and four blocked shots for the Suns, who played with O'Neal watching from the bench in street clothes.
"I just focus in on the game and what the game brings forth," Stoudemire said. "Each year I try to improve on something, last year was my jumper, this year it's defense."
The victory followed a similar struggle over Seattle on Friday.
"That was the big thing since the trade," D'Antoni said, "is get these two at home and then start working with Shaq tomorrow and see where we are. ... This was kind of a stopgap until we get to the real stuff."
Washington trailed nearly the entire game but never by more than 10 points.
"We fought and did everything we could to stay in the game," coach Eddie Jordan said, "and we just didn't make the plays coming down the stretch."
Nash's 3-pointer with 1:42 to play put Phoenix ahead 103-97, then his two free throws made it 105-99 with 30.7 seconds to go.
Jamison's two free throws sliced the lead to 106-104 with 8.8 seconds to play, then Stoudemire put it away with two from the foul line with 7.5 seconds left. He was 10-for-10 at the line and has made 30 free throws in a row to tie his career high.
DeShawn Stevenson sank a 3-pointer at the buzzer to make it a one-point finish.
"We're banged up, but everybody played hard," Haywood said. "This is one of those games you chalk up to just not having enough troops."
O'Neal, yet to play for Phoenix because of a hip injury that has sidelined him for two weeks, drew a huge ovation when he walked to the Suns' bench just before tipoff.
He worked out lightly before the game and was scheduled to practice on Monday. D'Antoni said he would meet with the big center and the trainer after Tuesday's practice to help determine when Shaq might make his debut with Phoenix.
The Suns have two games before the All-Star break -- Wednesday at Golden State and Thursday at home against Dallas.
The Wizards trailed 80-73 after Bell's 3-pointer with 2:48 to play in the third.
But Roger Mason sank consecutive 3-pointers to put Washington ahead 81-80 with 53.3 seconds to go in the quarter, the Wizards' first and only lead since it was 4-2.
Bell put the Suns back on top with a 3-pointer, then made two free throws with 3.3 seconds remaining and Phoenix led 85-81 going into the fourth.
Washington never caught up again. Stoudemire's steal and layup capped a 7-0 spurt that gave the Suns a 96-87 lead with 7:36 to play.
Stoudemire made his first seven shots, including his fourth 3-pointer of the season -- in 20 attempts. His first miss was a fastbreak layup that rolled off the rim at the halftime buzzer.
- The Suns' Leandro Barbosa was 2-for-12 shooting before leaving the game early in the fourth quarter with flu-like symptoms.
- Phoenix is 8-0 when Bell scores at least 20 points.
- The Wizards won at Phoenix each of the two previous seasons.
- Nash needs one assist to pass Nate Archibald to 18th on the NBA career list.
- The Suns are 21 games over .500 for the first time this season.