Rodney McGruder finished with 15 points and 11 rebounds, and Will Spradling scored 10 for the Wildcats (7-1), who played their first true road game this season.
Dwayne Smith scored 14 points and Isaiah Armwood had 12 points and 10 rebounds for the Colonials (4-5), who hosted their first BCS program since the 2009-10 season.
Kansas State defeated George Washington 69-56 on its home court last season.
The Wildcats let a seven-point second-half lead slip away but jumped ahead for good on Nino Williams’ putback with 3:18 remaining. Rodriguez was fouled while attempting a 3-pointer with Kansas State ahead 58-57, and he sank all three free throws with 1:46 left.
After Armwood made 3 of 4 free throws for the Colonials, Rodriguez’s jumper with 1:03 left pushed the lead back to 63-60, but he missed a one-and-one free throw with 26 seconds left.
Joe McDonald’s layup cut the lead to one, but Spradling made two free throws, putting Kansas State up by three with 13 seconds left. Smith’s 3-point try with 2 seconds remaining went long.
The Wildcats grabbed 24 offensive rebounds and finished with a 46-36 edge on the glass.
Trailing 29-27 at halftime and by four early in the second half, the Wildcats surged ahead 44-37 with a 15-4 spurt, which included two Spradling 3-pointers. The Colonials countered with a 13-4 run, going ahead 50-48 on Smith’s 3-point play with 9:03 remaining.
Lasan Kromah scored 12 points and Patricio Garino 10 for the Colonials, losers of two straight.
George Washington turned a 9-2 spurt first half spurt into a 25-18 lead, the Colonials’ largest of the game. McGruder stopped the run with a 3-pointer and the D.C. native tallied 12 points in the first half. Kansas State grabbed 25 rebounds before halftime but shot only 31.6 percent and trailed George Washington 29-27 at the break.