The win extended Miami's (22-3, 13-0 ACC) winning streak to 14 games and kept them undefeated in the ACC.
Johnson, who made 4-of-7 from the field, scored on a play called on the sidelines during a timeout called after Evan Nolte of Virginia (18-8, 8-5) tied the score 50-50 with a 3-point bucket with 14 seconds to play.
Shane Larkin led the Hurricanes with 11 points and six assists. Rion Brown was the only other Miami player in double figures with 10.
Joe Harris was the workhorse for Virginia. Harris scored 16 points and had seven rebounds. He was 7-of-16 from the field. Akil Mitchell took 10 shots from the field and chalked up six points in the game.
2014: The Year in Music [PHOTOS]