Without Garnett to guard him, Stoudemire scored 18 on 9-of-10 shooting in the first quarter and finished 11 of 14 from the field. Foul trouble kept him from adding significantly to his statistics.
Frye had a season best in scoring, sinking 6-of-9 3-pointers and grabbing 10 rebounds as the Suns swept the two-game season series.
"It's a win over the Celtics. We'll take it," Phoenix coach Alvin Gentry said. "They don't really put an asterisk by it and say Kevin Garnett wasn't here, so we'll take it any way we can get it."
"When you take your best two scorers off the floor against a scoring basketball team, and your best defender off the floor, you may not win that game," Boston coach Doc Rivers said. "So this game doesn't affect me at all."
"The lesson that's learned on this trip is not from tonight," Rivers said. "The lesson that we should learn on this trip is when you give away a game with the Clippers when you're healthy, then you do it again, then when you're injured you need those games back."
The Suns, who improved to 13-2 at home, never trailed after a 16-0 first-quarter run.
"They tried to play the [pick and] roll, they didn't want me to score inside the paint and I was able to get the jumper going," Stoudemire said. "When the jumper starts falling, then it's tough to defend us."
It is Boston's longest losing streak since dropping four straight last Jan. 4-9.
Boston was without Pierce for the fourth straight game with a knee infection. Garnett joined him on the sidelines Wednesday with a hyperextended right knee.
Rivers said Garnett was hurt in the loss to the Clippers on Sunday and didn't look right in the loss at Golden State on Monday.
The 16-0 run put Phoenix up 24-12 on Stoudemire's 7-foot bank shot on a pass from Steve Nash.
The Suns stretched it to 38-23 after Barbosa's 21-footer with 8:47 left in the half. Barbosa sank a 31-footer as the shot clock expired to put Phoenix up 44-30 6:21 from the break.
"We came out kind of lollygagging, going through the motions, and they came out playing hard," House said, "and they got us."
Boston cut the lead to 48-39 on House's 3-pointer with 3 1/2 minutes to go in the half, but Kendrick Perkins drew a technical foul that stemmed the momentum.
"We cut it to nine points and then he gets a tech," Rivers said, "I have no idea over what. He's got to grow up. He's got to get better."
Stoudemire scored four, Frye sank a 3-pointer and Jason Richardson scored six in a 13-2 run in the third. Richardson capped the spurt with a 22-footer that put Phoenix ahead 77-57 with 4:43 left in the quarter.
The Celtics were 13-1 on the road before their trip West. ... Boston had lost by no more than 11 in its seven losses going into the game. ... Frye matched his season high in 3-pointers. ... Phoenix is the second team to sweep a season series with the Celtics since the 2007-08 season. The Los Angeles Lakers did it last season. ... Besides House, the rest of the Celtics made 1 of 14 3-pointers. ... Boston plays at home against Toronto on Saturday, then has three days off before hitting the road again.