Without Garnett to slow him, Stoudemire scored 18 points on 9-of-10 shooting in the first quarter and finished 11 of 14 from the field.
Frye notched his season-best in scoring, making 6-of-9 three-pointers and grabbing 10 rebounds.
Garnett was sidelined by a hyperextended right knee.
The Celtics were missing Pierce for the fourth game in a row because of an injured right knee.
Rivers said Garnett's injury had nothing to do with the knee problems that kept him out of last year's Eastern Conference semi-finals against Orlando.
"My only issue is, how long is it going to take to get him right from this?" Rivers said. "A week, three days, four days? We don't know."
Rivers said he was also keeping a close eye on guard Rajon Rondo, who started against the Suns despite a sore hamstring.
Rondo played 32 minutes and scored 13 points.
"It's funny, as far as injuries go, I'm actually far more concerned with his than with Kevin's," Rivers said. "Kevin is sitting down, but Rondo I'm watching closely, because with a hamstring, that's a tough injury."
The Celtics now return home to host Toronto on Saturday.
Source: AFP American Edition