The Indians' magic number dropped to two after Detroit lost earlier to Kansas City. They could have lowered it to one, but now have to win their home finale Sunday and hope the Tigers lose again for Cleveland to clinch the division in front of its fans.
Melky Cabrera and Jose Abreu hit RBI singles in the first off Cody Anderson (2-5), and Todd Frazier connected for his 39th homer in the sixth as the White Sox snapped a six-game losing streak.
Quintana (13-11) gave up one run in six innings and beat Cleveland for the second time in 11 days.