The win was the 400th in the coaching career of Jim Crews.
Two free throws by Jeremiah Jones put Duquesne in front at 72-70 with 57 seconds remaining, but McBrook quickly hit a 3-pointer and the Billikens did not trail again.
Mike McCall boosted St. Louis in front by three with two foul shots that came with 13 seconds left and Micah Mason then missed a 3-point try for the Dukes.
St. Louis made 50 percent from the field and hit 10-of-19 from 3-point range, but still struggled to get past a team that has only a breakeven record this season.
McCall scored 13 points to lead St. Louis (18-2, 5-0 Atlantic-10 Conference). Gandy Glaze added 11 points for the Billikens.
Duquesne (8-8, 1-4 A-10) was paced by 18 points from Ovie Soko.