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.
Gonzaga center Przemek Karnowski, who missed most of last season with a back injury, says he is returning for another year.
Wisconsin forward Nigel Hayes has withdrawn from the NBA draft and will return to the Badgers for his senior season.
Recruiting reporter Jeff Borzello has gotten grilled for his selections of underachieving and overachieving college basketball programs. He joins Phil Murphy to explain his rankings.