Pekovic provided 16 points and 10 rebounds while Ricky Rubio supplied 13 points, 10 assists and five steals as Minnesota won for just the second time in 12 games.
Alexey Shved, Derrick Williams (12 points apiece) and Mickael Gelabale (11) also played big roles in the T-Wolves' win.
The Cavaliers got 20 points and seven assists from Kyrie Irving but couldn't avoid a second straight loss.
Tristan Thompson contributed 16 points and nine rebounds for Cleveland.
2014 amfAR Inspiration Gala [PHOTOS]
Julius Randle breaks leg during NBA debut