The Terrapins had trouble shaking Davidson until the latter stages of the second half but were deep enough to prevail and improve to 25-8. Maryland draws Butler, which dispatched Old Dominion 57-46 on Thursday, in a second-round game Saturday.
Davidson was sent home with a 29-5 record.
Freshman Stephen Curry, with a game high 30 points, kept the Wildcats in the game with sharp three-point shooting. He had five points in a 9-0 Davidson run to open the second half that gave the Wildcats a 52-44 lead.
But Maryland answered with an 8-0 spurt and tied the score. The game remained close with the Terrapins building a 67-63 lead with about eight minutes to go.
Davidson got within three points but Jones connected from three-point range with about two minutes left to put Maryland far enough ahead that the Terrapins were able to use free throws to increase their lead.
Maryland showed balance in scoring with Jones' 17 points backed by 12 each from D.J. Strawberry and James Gist and 11 points from Ekene Ibekwe, who also had 10 rebounds.