Mike Scott had 11 points and 13 rebounds for the ninth-seeded Cavaliers (15-15), who won their first game in a month and their first tournament game in four years. Virginia had lost nine straight heading into Greensboro, but pushed ahead late in the first half and led by as many as 11 points midway through the second half.
Virginia hadn't won a tournament game since beating Virginia Tech in the first round of the 2006 tournament in Greensboro.
Now the Cavaliers and first-year coach Tony Bennett are headed to Friday's quarterfinals to face fourth-ranked Duke, the tournament's top seed.
Rakim Sanders tied a season-high with 22 points for the eighth-seeded Eagles (15-16).
Boston College's Joe Trapani (12) gets his hand on the ball as Virginia's Jerome Meyinsse (55) goes to the rim as Boston College's Evan Ravenel (24) and Reggie Jackson (0) defend during the first half of an NCAA college basketball game in the Atlanti
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