Akil Mitchell provided 11 points and nine rebounds for the Cavaliers (23-11) who now move on to the NIT quarterfinals where they will go up against third-seeded Iowa Wednesday.
Taylor Barnette (13 points) and Mike Tobey (10) also reached double figures in the victory, which saw Virginia pull away in the second half and coast to the win.
Fifth-seeded St. John's (17-16) was paced by Phil Greene IV with 18 points.
Jakarr Sampson helped out with 14 points and six rebounds in the loss.
Puzzle-maker slips 'Murdoch Is Evil' into Rupert Murdoch's Sunday Telegraph
Reindeer recovered after escaping from Santa during lighting ceremony