The game, played at the RBC Center in Raleigh, N.C., was part of the Midwest Region, where the Hoyas (28-5) are the second seed.
After Georgetown opened with a 5-0 spurt, UMBC came within 18-17 on Brian Hodges' three-pointer with 8:09 left in the first half. GU eventually built a 34-22 halftime advantage and toyed with their heavy underdog opponents in the second half in a workman-like outing.
On Sunday, the Hoyas face Davidson.
UMBC was led by Darryl Proctor's 16 points and 10 rebounds.
Hodges scored 11 for the Retrievers (24-9), who were in their first NCAA Tournament game since they moved up to Division I in 1986.