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.
College basketball fans should be excited about next season's Jimmy V Classic, an event that will feature Duke's heralded freshman class.
Jeff Goodman logs all the coaching changes following the 2015-16 college basketball season.
Can Josh Pastner keep top talent in Georgia? Will Tubby Smith change his recruiting philosophy at Memphis? New coaches face some difficult questions.