Morrow (4-4) lasted seven innings, giving up four hits and a run to help snap a two-game Toronto skid.
Ronny Cedeno singled in the Pittsburgh run in the fifth, but Matt Diaz was thrown out at third on the play and Eric Fryer then became one of Morrow's strikeout victims to prevent further damage.
Eric Thames tied it with a leadoff homer in the sixth and the Blue Jays took the lead one inning later on back-to-back, one-out doubles by Rajai Davis and Escobar.
Paul Maholm (4-9) allowed both runs on nine hits over seven innings to take the loss.
Celebrity Families of 2014 [PHOTOS]