Francisco cranked a solo shot, his eighth, in the first inning and a two-run double in the fourth. Mulhern belted a three-run homer, his 14th, in the third, and Ginter drilled a two-run blast, his 12th, in the seventh.
Mike Rouse went 2-for-4 with a triple and an RBI for the Bisons (63-57).
Buffalo starter Jeremy Sowers (2-5) gave up three runs on eight hits and a walk with seven strikeouts over seven innings for his first win since tossing a complete game July 20.
Alberto Gonzalez went 4-for-4 with an RBI double in the first and Bronson Sardinha lined a run-scoring double in the second and a solo homer, his ninth, in the eighth for the Yankees (68-53).
Scranton/Wilkes-Barre starter Ben Kozlowski (3-7) surrendered four runs on five hits and three walks with a strikeout over three frames.