Sam Grooms' layup with 13 seconds left had forged a 50-50 tie for the Sooners, but Amath M'Baye fouled Rodriguez 8 seconds later and he made both free throws for the final margin.
Grooms had scored five straight points down the stretch to tie it up, but his 3-point try at the buzzer missed, and the Wildcats (17-4, 6-2 Big 12) hung on for their second straight win following consecutive losses to No. 1 Kansas and Iowa State last month.
Will Spradling scored 12 points and Martavious Irving added 10 to lead KSU.
Romero Osby provided 13 points and seven rebounds for Oklahoma (14-6, 5-3).