Miami lost its fifth straight, the last four without All-Star Dwyane Wade, sidelined with a sprained right wrist.
"It was one of those games you can't really talk much about because they were missing most of their guys," Suns coach Mike D'Antoni said.
Alonzo Mourning scored 15 points and grabbed six rebounds to become Miami's career leader in rebounds with 4,545, one more than the record previously held by Rony Seikaly. The Heat were without five players, plus coach Pat Riley, in the opener of a six-game road trip.
"This is the NBA, man," the Heat's Jason Kapono said. "They aren't going to postpone any games. We've just got to go out and try to get wins."
Phoenix's Leandro Barbosa, starting because Raja Bell was suspended for a game for kicking Toronto's Andrea Bargnani, was 7-for-8 shooting for 18 points despite a bout with the flu that caused him to miss the morning shootaround.
Marcus Banks, out of the Phoenix rotation in recent weeks, scored 13, including a 39-foot bank shot at the third-quarter buzzer. James Jones added 10 points for the Suns in the opener of a five-game homestand.
"You just want to stay aggressive," Nash said, "especially on nights when you know the energy won't be there for everyone, even in the building."
The Suns, just back from a 3-0 trip to the East, took the lead for good with a 15-0 first-quarter run, going up 22-14 on Nash's inside basket on a pass from Stoudemire with 3:24 left in the first quarter.
The lead reached 60-44 on Jones' second 3-pointer of the night with 1:19 left in the half. Phoenix led 60-45 at the break.
The Suns were up by as many as 19 in the third quarter, but Payton made consecutive 3-pointers to cut it to 80-71 with 38.8 seconds left in the period. After a Miami turnover, Banks banked in a shot just inside midcourt to put Phoenix up 83-71 entering the fourth.
The Suns scored the first five points of the final quarter, taking an 88-71 lead after Stoudemire stole the ball and drove downcourt for a layup with 10:47 to play.
That was it for Miami.
"We turned the ball over 20 times for 28 points," acting Heat coach Ron Rothstein said. "That's basically the game."
The Heat have Shaquille O'Neal sidelined while recovering from knee surgery, Wayne Simien out with a salmonella infection and two others -- Antoine Walker and James Posey -- inactive for failing to meet body fat requirements.
Riley took an indefinite leave of absence Wednesday with hip and knee problems.
"It's frustrating to see my teammates go through what they're going through," said Wade, who hopes to get back on the court soon.
"We'll see what happens tomorrow or the day after that," he said. "It's really day to day. It's getting better. It all depends on how much pain I have to play with."
Riley had three large pieces of cartilage removed from his right knee on Friday. There is no timetable for his return. ... The Heat are 1-8 without Wade and O'Neal since they began playing together in the 2004-05 season, including 0-6 this season. ... The game was played in front of the Suns' 40th consecutive sellout crowd at home. ... Miami had 10 players in uniform. ... Phoenix is 23-3 since starting the season 1-5.