The Jayhawks won their seventh in a row and remained unbeaten in the Big 12 Conference.
Iowa State, trying for a breakthrough win on Kansas' home floor, was within a point after Georges Niang made a long-range shot with 4:30 to play.
Joel Embiid next scored on a dunk for Kansas and Wiggins then went to work, hitting two free throws, scoring on a tip-in and finishing off a drive with a dunk that gave the Jayhawks an 81-72 lead with 2:49 remaining.
Wiggins led Kansas (16-4, 7-0 Big 12) with 29 points, hitting 10-of-16 from the field. He also grabbed seven rebounds.
Perry Ellis contributed 20 points for Kansas and Embiid had 14.
Niang scored 24 points for the Cyclones (15-4, 3-4 Big 12).