The Mariners erased a 3-2 deficit in the sixth on an Eric Thames solo shot off Cleveland starter Ubaldo Jimenez.
After Brendan Ryan drew a lead-off walk against Joe Smith (7-4) in the seventh, Tony Sipp came on in relief and, one later, Saunders blasted a 2-1 pitch over the center-field wall for the decisive blow.
The clout made a winner of Charlie Furbush (5-2) who tossed two shutout innings in relief of starter Kevin Millwood.
Tom Wilhelmsen gained his 18th save despite allowing two hits and a walk in the ninth as Seattle notched its sixth straight win in the opener of a three-game series.
Jason Kipnis socked a solo homer and added a run-scoring single for the Indians.
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