Jesus Montero led off the 12th with a double off Addison Reed (0-1) and pinch-runner Munenori Kawasaki came across with the go-ahead run when Jaso drove a pitch into the right-center field gap for a double.
The Mariners catcher also scored when the next batter, Chone Figgins, singled to left.
The Mariners snapped Chicago's nine-game winning streak.
Michael Saunders went 4-for-6 with a two-run homer and Ichiro Suzuki contributed a pair of solo shots for the Mariners, who evened their three-game series and broke a seven-game skid against the Chisox.
Tom Wilhelmsen (2-1) earned the victory with three scoreless relief frames and Hisashi Iwakuma notched his second save for Seattle.
Alex Rios and Dayan Viciedo also went deep for the losers.