James Harden scored 33 points and had 12 assists for Houston, which saw its nine-game winning streak end.
Ricky Rubio tied his own franchise record with 17 assists to go with 10 points.
Wiggins carried Minnesota early, scoring 15 first-quarter points as the Wolves opened up an 11-point lead. Muhammad provided six quick points early in the second quarter and energized the crowd with a transition dunk.
Ryan Anderson's 3-pointer gave Houston a 69-68 lead midway through the third quarter, but Minnesota followed with a 17-4 run capped by a thunderous dunk by Towns. The Wolves ended the third quarter leading 89-77.
They started the final quarter scoring the first eight points to put the game out of reach.
Rockets: The Rockets had a nine-game winning streak the last time they came to Minnesota. They came from behind to win 111-109 in overtime on Dec. 17 to push that streak to 10. ... Anderson hit three 3-pointers in the fourth quarter and finished 5 of 14 from beyond the arc.
Timberwolves: Zach LaVine missed the game with a left hip contusion. He was injured in Monday's game against Dallas. . Brandon Rush started in his place and scored 12 points, hitting four 3-pointers, three assists, three rebounds, three steals and two blocked shots. ... Rubio passed Sam Mitchell to move into fourth place on the team's career games played list with 292. ...Towns had his 29th double-double of the season, third-best in the league.
Rockets: Houston returns home to face the Memphis Grizzlies on Friday before hitting the road again for their next its next two games.
Timberwolves: Oklahoma City visits Minneapolis on Friday night as the Wolves wrap up a three-game home stand.