The Cowboys (17-9, 6-6 Big 12) also got 20 points from James Anderson.
A 4-point play by Carter with 7:19 remaining gave the Bears a 64-63 lead, but Oklahoma State outscored Baylor 20-11 the rest of the way.
The Cowboys' closing run was fueled by Eaton, who drained a 3-pointer and converted a lay-up in traffic.
Oklahoma State hit just 6-of-18 from 3-point range, but converted 28-of-33 free throws and outrebounded Baylor 39-30.
Baylor was 13-of-31 from 3-point range.