Sowers (3-7), recalled from Triple-A prior to the game, allowed just four hits and two walks.
Franklin Gutierrez was 2-for-3 with a walk for the Mariners, who have lost three of five.
Erik Bedard (5-3), who lasted only three innings, is winless in four starts since coming off the disabled list.
Chris Jakubauskas relieved Bedard in the fourth and gave up a two-run homer to Gimenez. Two RBI singles gave Cleveland a 6-0 lead and Cabrera's homer made it 8-0.