Saunders led off the ninth with a single off Tyler Robertson (1-1), Brendan Ryan reached on a bunt single and Dustin Ackley drew a walk to load the bases with none out.
Casey Fien came in to pitch and Jaso greeted him by sending fly ball into left field, allowing Saunders to come home with the winning run.
The rally made a winner of Tom Wilhelmsen (4-2), who wiggled out of a two-out, bases-loaded jam in the top of ninth by inducing Josh Willingham to fly out.
Justin Smoak socked a solo homer for the Mariners, who clinched their three-run series.
Willingham and Joe Mauer drove in runs for Minnesota.