The Wildcats (21-10) finished fifth in the Big 12 and were bounced in their opening game of the conference tournament by Baylor. But two wins over Missouri and a road victory over the Bears in the regular season locked up their at-large bid.
The winner will likely face No. 1 seed Syracuse.
It's the third straight appearance for Kansas State under coach Frank Martin and the fourth in five seasons after taking over for Bob Huggins.
The Wildcats lost to Wisconsin in the third round last season and to eventual runner-up Butler in the 2010 regional finals.