Rhode Island led 11-9 on a dunk by Martin, but Duquesne used a 14-2 run to lead 27-19 at halftime.
The Rams rallied in the second half, tying it at 49 on a 3-pointer by Matthews, but the Dukes use an 11-4 run to lead 58-53 with 4:51 left. Matthews put the Rams up 59-58 with another 3 with 1:14 to go, then Terrell made the go-ahead free throw. The Dukes had a chance to win, but Derrick Colter's jumper missed.
Micah Mason scored 18 for Duquesne (6-8, 1-2) and Colter had 15.