Heckmann's reverse lay-up with 46 seconds remaining the extra time boosted the Eagles to a 58-57 lead and Lonnie Jackson sank 4-of-4 free throws down the stretch to secure the improbable upset win, dashing the Orange's hopes for an undefeated season.
Olivier Hanlan led Boston College (7-19, 3-10 ACC) with 20 points and Jackson finished with 10.
Ryan Anderson hauled down 14 rebounds to go with nine points for the Eagles, who had lost 15 of 18 games coming into the contest but connected on 11-of-22 tries from 3-point range in the stunner.
C.J. Fair netted 20 points and grabbed 11 rebounds for Syracuse (25-1, 12-1), which had managed to keep its perfect record intact with close wins over Pittsburgh and North Carolina State.
The Orange's loss left Wichita State as the only undefeated program remaining in Division I.
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