Morrow (2-1) scattered five hits over six scoreless frames, didn't issue a walk and struck out nine in a dominating performance. The right-hander placed 66 of his 104 pitches for strikes.
Encarnacion's bases-loaded blast came in the eighth inning and gave him five RBI for the game.
Adam Lind went 2-for-3 with a run-scoring double for Toronto.
Seattle starter Kevin Millwood (0-2) allowed only one earned run over seven innings, yielding seven hits to absorb the loss.
Celebrity Families of 2014 [PHOTOS]