Kelley scored 12 points to help give Sacred Heart a 25-11 lead with 13:50 left in the first half, and the Pioneers led by double digits the rest of the way.
Phil Gaetano dished out seven assists and Falzon had eight boards to lead the Pioneers, who outrebounded Mitchell 42-29.
Sacred Heart (5-4) has already matched last seasons' win total in just its ninth game.
Parris Hill scored 25 points on 9-of-20 shooting from the floor to lead Mitchell. Donavan McClean and Frank Martin both added 11 points.