Minnesota (3-5) fell behind by 14 points early, only to regroup in its third game in four nights for its second win in as many nights.
"I felt like we were a little lackadaisical the first half, but I knew if we run our stuff and brought some energy we could get a win. That's what we have to do," said Corey Brewer, who had 15 points and eight rebounds for the Timberwolves.
Jonny Flynn led Minnesota with 16 points and five assists, while Ryan Gomes and Ryan Hollins added 14 points each.
Chris Bosh had 27 points and 14 rebounds and Jose Calderon added 17 points and six rebounds for Toronto (2-6) in its fourth straight loss.
The Timberwolves, playing without big men Kevin Love (hand) and Al Jefferson (flu-like symptoms), took over in the third quarter and weathered a late rally.
"This is our third game in four nights and the guys are tired and we're traveling around and you can make every excuse you want," first-year Timberwolves coach Kurt Rambis said. "But the great players and the great teams find a way to dig down deeper and find a way to win ballgames.
"Players have to understand that part of being a professional is being able to deliver night in and night out."
An 11-2 run pushed the Timberwolves to an 11-point lead in the third quarter. The surge came with Toronto's leading preseason scorer, Andrea Bergnani (13.0) on the bench after getting his fourth foul less than two minutes into the period and didn't return until the fourth.
Bosh took over, scoring nine of Toronto's 16 points in the quarter.
"We got hesitant and had too many turnovers in the second half," Toronto coach Jay Triano said. "You've got to take care of the ball."
The Raptors finished with 22 turnovers; Minnesota had 15.
Flynn scored on a drive and Brewer had a three-point play on a breakaway with about 5 minutes to play to put the Timberwolves in control.
DeMar DeRozan's drive with 5:47 remaining gave Toronto its largest lead of the first half, 38-30. Flynn scored six of Minnesota's final eight points to pull the Timberwolves within 46-44 at halftime.
Ten of the Timberwolves played at least 15 minutes.
"It's a great confidence boost for everyone to play without our best player (Jefferson) and another focal point in Kevin Love, so when they come back we'll be a much stronger unit," Gomes said.