With the score tied 1-1, Kalish pinch-hit for Brent Lillibridge and doubled with one out off Brandon League (0-5), moving to third on Dustin Pedroia's single.
Lucas Luetge came in to pitch and Ortiz greeted him by driving a long fly to right fielder Ichiro Suzuki, scoring Kalish without a throw.
Pedrioa added a solo shot for Boston.
Mariners starter Jason Vargas hurled eight innings of one-run ball, allowing five hits while walking two and striking out six.
Suzuki supplied Seattle's only RBI.