Slowey (9-3) limited the Yankees (68-52) to one run on seven hits and two walks while striking out five. The 23-year-old right-hander won for the first time since July 17 and lowered his International League-leading ERA to 1.77.
Jason Miller replaced Slowey with runners on first and second and retired Eric Duncan on a lineout before Jerome Williams came on and got pinch-hitter Bronson Sardinha to fly out and notch his first save for the Red Wings (67-55).
Lew Ford was 3-for-3 with a walk and two runs scored and Jose Morales lined a two-run triple in the eighth for Rochester, which has won eight of 10 meetings with Scranton/Wilkes-Barre this season.
Yankees starter Kei Igawa (3-4) gave up two runs on eight hits while fanning six in six frames.
Duncan had two hits and scored the Yankees' only run on Kevin Thompson's groundout in the third.