Nate Duhon led the Cougars (7-16, 2-2) with 14 points, and Matt Ross had 13.
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.
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