Trailing 2-0 entering their final at-bat, the Mariners came up with three runs to stun the Tigers and pull out a win in the first of a three-game series at Safeco Field.
The next batter, Jesus Montero, stroked a double to chase home Suzuki with the with the tying run.
Duane Below came in to pitch and Kyle Seager sacrificed pinch-runner Munenori Kawasaki to third. Jaso finished the rally with a game-winning sacrifice fly to right.
The comeback made a winner of Steve Delabar (1-0), who tossed a scoreless top of the ninth for the Mariners.
Tigers starter Doug Fister, making his first start since April 7 following a stint on the disabled list, hurled seven shutout innings, allowing four hits.
Prince Fielder had two hits and an RBI for Detroit.