Markel Starks had 14 points and seven assists while Jabril Trawick added 12 points for the fourth-seeded Hoyas (18-14), who will play Florida State in the next round.
Juwan Staten tallied 23 points and seven assists, while Terry Henderson chipped in 13 points off the bench for the Mountaineers (17-16). Remi Dibo logged 11 points and Eron Harris finished with 10, while Devin Williams cleared eight boards.
West Virginia shot 54.5 percent from the field in the first half as it led 33-30 at the break. Georgetown made 37 percent of its field goal tries and attempted five more shots than WVU.
The Hoyas got hot in the second half as they connected on 52 percent of their field goal attempts and went 17-of-21 at the free-throw line. The Mountaineers cooled down and connected on just 37 percent of their shots from the floor. Georgetown went on an 11-0 run midway through the stanza to take a commanding 68-51 lead.
Georgetown played better inside as it outscored the Mountaineers in the paint, 32-22.