Moyer (15-5) became the third 15-game winner in the American League, tying the mark set by Toronto's Roy Halladay and Oakland's Mark Mulder.
Seattle (69-43) improved to 6-1 against the Indians in 2003.
Cleveland (45-67) scored its lone run in the third inning on a Jhonny Peralta solo homer.
C.C. Sabathia got the start for Cleveland and went deep into the game in hopes that his offense would come from behind and get him off the hook. In eight innings, the huge left-hander surrendered only two runs on nine hits, but received the hard-luck loss nonetheless.
Sabathia fell to 9-7.
Seattle scored its runs with a one-spot in both the first and third innings. Ichiro Suzuki tripled and scored on a throwing error to lead off the game, putting the M's up 1-0 immediately. Two innings later, the M's tacked on another run when John Olerud racked up a RBI by drawing a bases loaded walk.
Ichiro went 3-4 to lead the Mariners' 10-hit attack. Three others had two hits for the visitors from Seattle.