DeJesus delivered a sacrifice fly in the third inning, putting Oakland ahead 2-0, and added an RBI single in the fifth for a 3-1 advantage as the A's completed a three-game sweep of Seattle.
Ryan Sweeney provided a two-run triple in the seventh and scored on a wild pitch for Oakland.
Trevor Cahill (10-13) was the winning pitcher after producing five innings of one-run ball during which he walked two and struck out four. Five A's relievers were nicked by the Mariners for four runs on eight hits the rest of the way.
Seattle's Blake Beavan (3-5) was tagged for four runs on seven hits in a five-inning start.
Dustin Ackley hit a two-run homer and Luis Rodriguez added a two-run single in the ninth for the Mariners.