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.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.