Trailing 4-3 entering the fifth, the Blue Jays scored three times to grab control of the contest -- all with two outs.
Rajai Davis singled and went to third on an Anthony Gose double off Athletics starter Tommy Milone (9-9).
After Edwin Encarnacion was intentionally walked to get to Escobar, the Toronto shortstop made the A's pay by scorching a 1-2 pitch through the hole, scoring two runs.
Kelly Johnson followed with another single to chase home Encarnacion (2-for-4, homer) with what turned out to be the winning run.
Aaron Laffey (3-2) earned the triumph after yielding four runs on six hits over six innings. Aaron Loup, Steve Delabar and Casey Janssen (14th save) combined to secure the win with two scoreless frames.
The victory earned the Blue Jays a split in their four-game series.
Josh Reddick slammed a three-run homer for the A's.
Senate Democrats to pull all-nighter on climate change
Interpol investigating stolen passports on missing flight