Council had made just 5 of 27 3s coming into the game, but took advantage of open looks early then largely carried the Jayhawks (8-3) down the stretch - including scoring Kansas' last 13 points of regulation and feeding Flory Bidunga's go-ahead dunk with 51.9 seconds left in the OT.
N.C. State (7-4) had one final possession to win it, inbounding from near halfcourt with 1.0 seconds left. But Darrion Williams' fading 3 on the catch missed everything to end this one.
Kansas freshman star Darryn Peterson had 17 points, five rebounds and four assists. But he abruptly checked out of a tight game with 2:15 left and didn't return, watching from the bench in an exit coming shortly after he missed seven games with a hamstring strain.
Council finished 13 of 27 from the floor and 9 of 15 from behind the arc to go with seven rebounds and four assists.
Quadir Copeland scored 19 points to lead the Wolfpack, while Williams finished with 17 points and 10 rebounds.
Texas Southern visits the Wolfpack on Wednesday.
The Associated Press contributed.
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