The sixth-seeded Rams (19-12) led 31-29 at halftime before going 11 of 22 from the field in the second half to advance to the quarterfinals against No. 3 seed Richmond on Friday.
Delroy scored 14 of his points in the first half, and Nikola Malesevic took over in the second, scoring all 11 of his points.
Rhode Island, which trailed by as many as six points in the first half, led 35-34 with 17:27 left in the game. The Rams then pulled away for good on an 11-2 run, capped by Akeem Richmond’s 3 with 10:53 to play.
Richmond finished with 15 points and Marquis Jones added 10 for Rhode Island.
The 11th-seeded Billikens (12-19) were led by Mike McCall with 14 points.