Maryland (10-1) shot 68.4 percent from the floor in the first half as it won its second all-time meeting with the Peacocks.
Chazz Patterson led Saint Peter's (4-5) with 13 points. Forward Quadir Welton, who was averaging a team-high 16 points for the Peacocks, was held to five points on 2 of 11 shooting against the Terrapins.
Maryland opened on a 14-0 run, and Saint Peter's didn't score its first points until 11:56 remained in the first half. The Peacocks never cut the margin to less than 10 the rest of the way.
The Terps held a 14-5 scoring advantage off turnovers.
Maryland welcomes Jacksonville State for a 7 p.m. tilt at XFINITY Center Monday.