Frye scored a game-high 33 points and hit a 3-pointer with 2:05 left in overtime to start an 8-0 run and the Suns rallied to beat Minnesota 135-127 for the Timberwolves' 14th consecutive loss.
"Coming home, seeing the family and getting in a comfortable environment rejuvenated me," said Frye, who set a Suns' regular-season record with nine 3-pointers, four more than he had during Phoenix's recent five-game road trip.
"I just wanted to be a little more aggressive tonight."
After Anthony Randolph missed an 18-footer, Grant Hill scored on a 12-foot jumper with 1:27 remaining to give the Suns a four-point lead. Jared Dudley added a 3-pointer from the right corner with 47.2 seconds left to make it 131-124.
Hill had a chance to end the game in regulation but his catch-and-shoot 6-footer at the buzzer rolled off the back of the rim to keep the game tied at 121-121.
Dudley scored 26 points and Hill had 21 for the Suns, who snapped a two-game losing streak.
"It's a win. We'll take it," said Suns coach Alvin Gentry, whose team needs to beat San Antonio in Wednesday's season finale to reach the 40-win plateau for the seventh straight season. "We didn't anticipate that we would have to score 135 to win."
Michael Beasley scored 16 of his 26 points in the fourth quarter and overtime and Randolph added 24 for the Timberwolves, who led by 12 in the first half.
Phoenix took its first lead since the opening minutes when Dudley tipped home a Josh Childress miss with 1:02 left in the third quarter to put the Suns ahead 92-91.
"We didn't execute defensively the game plan, but we pulled it out and it took big shots to do it," Dudley said.
The Timberwolves opened the lead back to six at 106-100 on Randolph's 15-footer, but then the Suns' 3-point shooting took over.
Dudley tied the game at 108-108 with 3:58 left and Frye put the Suns back in front with another 3-pointer, this one from the top of the arc, with 3:22 to go.
Another Dudley 3-pointer made it 118-114 with 1:23 left in regulation.
"Channing Frye did what he do -- just knock down big shots," Beasley said. "When you crowd a guy like Steve Nash, it's hard to get out to shooters and protect the roll and then protect him. They killed us with everything."
Martell Webster briefly put the Timberwolves ahead 119-118 with a 3-pointer, but Nash hit a 3-pointer from the top of the arc to make it 121-119 with 27.3 seconds left.
Beasley had a chance to give Minnesota the lead when he was fouled on a layup by Hakim Warrick with 8.4 seconds left, but he missed the free throw off the back left of the rim to set up Hill's subsequent miss and send the game to overtime.
"It hurts," Beasley said. "I could have won the game with a free throw. It's going to haunt me tonight, but that's how it goes."
Nash had eight points and 16 assists to pull ahead of Rajon Rondo for the league's assists title with one game to go. Nash won the assist title in four of the past six seasons. ... The Suns were 18 of 29 from beyond the 3-point arc, including 8 of 11 in the fourth quarter and overtime. ... Luke Ridnour scored 21 points on 10 of 13 shooting for Minnesota. ... Phoenix swept the season series against the Timberwolves and has won six straight against Minnesota. ... The Timberwolves are winless on the road since March 2 and overall since March 11.