Elfrid Payton had 14 points, eight rebounds and five assists, and Andrew Nicholson scored 15 for the Magic (10-8), who have won four straight for the first time since December 2012.
"We’re good, man," guard Victor Oladipo said. "And I think we’re starting to believe that we’re good. We’re going into every game believing we can win. That’s the biggest thing we have to do from now on."
Andrew Wiggins scored 27 points for the Timberwolves (8-10), but missed a free throw with 5.6 seconds to play that would have tied the game. Minnesota shot just 37.7 percent and fell to 2-7 at home this season.
The Magic led by as many as 17 in the third quarter. Minnesota had it tied with 4:30 to play, but went 3:40 without a bucket late in the fourth.
"We’ve been in a lot of the games and we should definitely have won a lot of them," Wolves guard Zach LaVine said. "We’ve got to come out and play better in the first half."
The Magic won their previous three games by spreading the ball around on offense and clamping down defensively with tenacity on the perimeter and strength in the paint. All that was on display in the first half Tuesday night, when they jumped on a Timberwolves team that has not played with the same energy at home that it has on the road.
The Wolves missed 12 of their first 14 shots, and Evan Fournier and Vucevic pushed Orlando out to a 12-4 lead. Minnesota shot just 24 percent in the first quarter and turned the ball over nine times in the first half to fall behind by as many as 15 points.
"The only way to be a winning team is by defending," Vucevic said. "Some games we might go out there and outscore people, but we know that for us to be consistently winning we have to defend. There’ll be games where you’re not going to be able to score, go through a tough stretch where you can’t score even during a game."
A 24-10 run by the Wolves bench helped them surge back into the game, and Wiggins scored on a putback to tie it at 87 with 4:30 to play.
But Oladipo blew by LaVine for a dunk and hit a 3-pointer from the left wing, and Payton scored on a tough drive to the basket with 35 seconds to go to help secure a series sweep for Orlando.
Oladipo finished with 13 points.
"It puts a lot of pressure on your defense," Timberwolves interim coach Sam Mitchell said of the poor shooting. "You can’t make a mistake and you can’t foul. It’s just a lot of pressure."
TOWNS SITS AGAIN
Timberwolves center Karl-Anthony Towns, the No. 1 overall pick in the draft, spent the entire fourth quarter on the bench for the third straight game. He finished with six points on 2-for-11 shooting and six rebounds while Mitchell went with Gorgui Dieng, who had 11 points and seven rebounds. Towns hasn’t played more than 28 minutes in six straight games.
A reporter started to ask Mitchell about the decision after the game, but the coach angrily batted it aside.
"Man, don’t come ask me that question," Mitchell snapped. "Ask me a question about the game. Don’t ask me a question about playing time."
Magic: Tobias Harris had 13 points. … Orlando has won 13 of the last 15 against Minnesota. … Orlando is 4-4 in games decided by five points or fewer.
Timberwolves: Ricky Rubio came back from a two-game absence because of a sore left ankle. He had three points on 0-for-5 shooting and five assists in 27 minutes. … Kevin Garnett had four points and eight rebounds in 20 minutes, surpassing Jason Kidd (50,110) for third on the NBA’s career minutes list.