It was the 19th-straight win at home for the Cavaliers, who will host the No. 3 Iowa Hawkeyes for a chance to play in the NIT Semifinals at Madison Square Garden.
With junior guard Joe Harris, Virginia's leading scorer this season, having an off night, the Cavaliers got big contributions from a couple of role players on the team. Anderson averages 6.8 points per game and finished with a team-high 18. Barnette, who normally averages just 2.3 points a game, added 13 points in 13 minutes.
The Red Storm struggled from the field, hitting 34 percent of their shots and just 2-of-16 from the three-point line. Phil Greene IV led St. John's with 18 points but was just 1-of-6 from three-point range.
Three more games tomorrow will fill out the remainder of the quarterfinal bracket. Click here for CBS Sports' updated bracket.