Ryan Anderson added eight points and nine rebounds for BC (13-16, 5-11 Atlantic Coast Conference), which trailed almost all of the second half and by as many as 11 points with 10 minutes to play.
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Akil Mitchell had 16 points and eight rebounds and Joe Harris scored 14 for Virginia (20-9, 10-6). It was the second time in two weeks that BC has beaten a team coming off a victory over Duke.
BC trailed by five points, 51-46, with 1:38 left when Eddie Odio got underneath for a dunk and then blocked Joe Harris' jumper, setting Olivier Hanlan off on a fast break. Harris was sent to the line and made one of two free throws, then BC set up for the winning shot, working the ball around to Rahon.
The BC freshman swished the ball through as he was knocked to the floor by Evan Nolte. Rahon missed the free throw and Virginia's Jontel Evans brought the ball the length of the court before -- against tough defense by Patrick Heckmann -- stepping out of bounds on the baseline with 0.4 seconds left.
Mitchell stole the inbounds pass in the Virginia backcourt, took one dribble and fired up a shot -- too late -- from beyond the half-court line that went in.
Mitchell dropped to the floor in disappointment while the BC players celebrated.
After the traditional singing of the Boston College alma mater, the players headed over to press row to congratulate longtime assistant sports information director Dick Kelley, who received the Most Courageous Award from the U.S. Basketball Writers Association. Kelley is confined to a wheelchair with Lou Gehrig's disease.