Morrow (7-3) gave up singles to A.J. Pierzynski in both the second and eighth innings, struck out five and walked only two.
Morrow blanked the Los Angeles Angels May 5 and the New York Mets May 19. Prior to this season, Morrow's only shutout had come in 2010. This was his 83rd career start.
The first two runs were charged to Jose Quintana (1-1), who took the loss while giving up nine hits in six innings.
Toronto has won three in a row.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut