It took three late free throws by Steve Nash to seal the Suns' 13th consecutive victory over the Nets in Phoenix, 99-93, on Friday night.
Stoudemire rebounded from the second scoreless game of his NBA career with 25 points, 10 boards and seven blocked shots. Nash added 26 points and 13 assists in the Suns' fifth victory in six games and the Nets' fourth consecutive loss.
"I just played off my teammates," Stoudemire said. "Whatever the offense brought the defense on my side, I just took what was there."
Phoenix shot out to a 20-point first-quarter lead and was up by as many as 22 in the second and third. But as has been the Suns' habit so far this season, the lead dwindled in a hurry.
Nets coach Lawrence Frank benched his starters after three quarters, and the reserves rallied behind Williams, who scored 13 consecutive New Jersey points to cut it to 96-93 on a 20-footer with 21 seconds left.
Nash made two free throws with 18 seconds to play, then one of two with 12 seconds remaining after a Nets' turnover to seal the victory.
"For three quarters we played really well," Phoenix coach Mike D'Antoni said. "We're getting better each game. I have to get the bench straight. We're not finishing games real strong, and we will work on that."
Williams scored 21 of his 27 points in the fourth quarter.
"I got a couple of stops, I got a couple of baskets, and I got some confidence," he said.
Vince Carter added 23 points, but played only the final 29.5 seconds of the fourth quarter.
Jason Kidd had seven points, eight rebounds and five assists, shooting just 3-of-12, and sat out the fourth.
"That group that finished the game deserves a great deal of credit in their fight," Frank said.
He said he never considered putting his starters back in.
"We were going to either win or lose with that group," Frank said, "because they earned it."
Raja Bell made his first four shots, three of them 3-pointers, and scored 18 for Phoenix, which climbed to .500 (6-6) with the win. Shawn Marion added 16 points but missed two free throws with 29.5 seconds to play.
Stoudemire, who has been bothered by a cold and sore throat, took one shot and didn't score in the Suns' victory over New Orleans on Wednesday night, continuing what has been an up-and-down comeback from major knee surgery that kept him out of all but three games of last season.
The Suns were without Leandro Barbosa because of a sprained left ankle.
Phoenix shot 84 percent (16-for-19) in a 39-point first quarter. Nash had the only misses of the quarter but still went 5-for-8 for 12 points with six assists. Stoudemire, Bell and Marion were a combined 10-for-10 in the period.
The Suns, who never trailed, used a 14-0 run to go up 19-4 on Nash's two free throws. The lead twice reached 20 in the quarter.
Carter scored nine in the second quarter, including a three-point play after a Suns' turnover that cut Phoenix's lead to 53-41 with 1:35 left in the half.
But Marion sank an 11-footer, then after a New Jersey turnover, Nash made a 19-footer at the shot clock buzzer, with 5.6 seconds left in the half, and the Suns led 57-41 at the break.
"Most importantly we're playing harder and we're working on it," Nash said, "and we're making improvements."
The Suns shot 36 percent (20-for-55) in the final three quarters. ... Veteran Nets forward Cliff Robinson missed his third consecutive game with a sprained left knee. ... New Jersey matched its longest losing streak of last season. .... The last time the Nets won in Phoenix -- on March 13, 1993 -- their starting lineup was Drazen Petrovic, Derrick Coleman, Chucky Brown, Rumeal Robinson and Chris Dudley. ... Stoudemire's career high in blocks is 10 against Utah on Feb. 7, 2004.