Matt Humphrey had 13 points to lead Boston College (7-14, 2-5). The Eagles have lost four straight since beating Clemson and Virginia Tech in consecutive home games earlier this month.
The game was tied at 49 before Miami took control by scoring the 14 unanswered points.
The Hurricanes outscored Boston College 27-5 over the final 7 minutes.
Grant's 3-pointer from the top of the key -- the Hurricane's first of the second half -- pushed Miami ahead 52-49 with 6:17 to play.
Scott then had a steal and driving basket on the ensuing possession, and Grant hit another jumper to key the game-breaking spurt. Trey McKinney Jones nailed a 3 from the left wing, Grant hit two free throws after Boston College's Lonnie Jackson was whistled for a technical foul and Scott had another basket to cap the spree, making it 63-49 with 3:43 to play.
Miami led by three at halftime and pushed it to five twice early after intermission, the second coming on Kadji's driving basket that made it 38-33 before the Eagles scored the next seven points. Jackson started the spree with a 3 from the left corner -- his first basket of the game -- Jordan Daniels drove for a layup and Dennis Clifford banked in short jumper in the lane.
Kadji's put-back tied it at 40 with 14:16 to play. He scored Miami's first eight points of the second half.
The game was then tied four times over the next 7 minutes.
It was a matchup of two of the conference's top three 3-point shooting teams. The Hurricanes came in ranked second and Boston College next, but Miami missed 12 of its 16 attempts from beyond the arc in the first half. The Eagles fared much better in the opening 20 minutes, nailing 5 of 9.
Neither team held more than a four-point lead in a fairly cleanly played opening half. Miami opened a 19-15 edge on Johnson's tip-in basket midway and grabbed a 34-31 edge at the half after Johnson scored the final two buckets: one coming on a fall-away flip in the lane and the second a breakaway jam with 49 seconds left.
Boston College forward Patrick Heckmann missed the game due to an illness.
It was the opener of a men's-women's basketball doubleheader between the schools. No. 10 Miami faced the Eagles in the second game.
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