Evans' basket gave the Red Raiders a 63-62 lead. Aaron Ross and Niem Stevenson then combined for three foul shots for Texas Tech before Barry Brown made a 3-pointer in the final seconds for Kansas State.
Evans finished with 18 points. Zach Smith had 16 points and seven rebounds for the Red Raiders (13-3, 2-2 Big 12), who improved to 11-0 at home.
Kamau Stokes led Kansas State (13-3, 2-2) with 17 points. Dean Wade added 12 points, and D.J. Johnson finished with 11.