The Mariners were trailing 1-0 in the seventh when Bay connected off Angels starter Jason Vargas for a leadoff shot to make it 1-1. Morse pulled a 1-2 pitch from Vargas over the Angels bullpen and onto the left-field porch for the decisive blow with one out in the ninth.
The comeback made a winner of Carter Capps (2-1), who tossed two scoreless relief innings after starter Hisashi Iwakuma had held the Angels to one run over six innings.
Tom Wilhelmsen collected his eighth save with a 1-2-3 ninth as Seattle took three wins in a four-game set with Los Angeles.
Vargas (0-3) ended up yielding six hits and two walks in a complete-game loss.
Peter Bourjos got two hits for the Angels, who fell to 9-15.
Swim Week Miami Beach 2014 [PHOTOS]