Chicago State led 41-37 after Quinton Pippen's jumper 4 minutes into the second half, but an 18-4 run over the next 7 minutes, capped by two Provost free throws, put the Broncs ahead 55-45.
The Cougars pulled within 66-65 on Corey Gray's 3-pointer with 14 seconds left, but Provost made two more free throws before Gray missed a 3-pointer at the buzzer.
Chicago State still leads 7-5 in the all-time series between the schools, but Texas-Pan American has won the last three meetings.
Purdue coach Matt Painter says players haven't used the fifth-year graduate transfer rule for its true intent.
The 2017 recruiting class is short on point guards, with Trevon Duval leading only eight prospects from the ESPN 60 who are still available.
The dust has settled after players made their NBA draft decisions. Which college teams won? Which lost? Well, Villanova is pretty happy. USC, meanwhile, might not be as thrilled.