Morrow (4-1) won his fourth straight start, allowing one run on four hits while overcoming four walks.
The right-hander was given a lead in the fourth when Adam Lind blasted a two-run homer to break a scoreless tie.
J.P. Arencibia added a solo shot in the seventh and Edwin Encarnacion added his 10th of the year in the next frame as the Blue Jays broke a three-game skid and earned a split in their two-game set with the A's.
Oakland starter Tyson Ross (1-3) was touched for three runs on five hits over 5 2/3 innings.
Josh Reddick and Jonny Gomes drove in runs for the A's, who fell to 5-2 in May.