The Mariners halted the brief Los Angeles winning streak at two games and moved within one game of Texas for the lead in the American League West.
Bedard (4-4) struck out five and did not walk a batter. He escaped a two-on, two-out jam in the second and allowed only one other base runner through the seventh.
League gave up a one-out single in the ninth before collecting the save.
Carlos Peguero put Seattle in front with a two-run single in the seventh and Greg Halman hit his first major league homer in the eighth for the Mariners.
This was Halman's 51st career major league game scattered over three seasons, all with Seattle.
Ervin Santana (3-7) was saddled with the loss after giving up two runs on eight hits in 6 2/3. Santana struck out seven.
Swim Week Miami Beach 2014 [PHOTOS]