Morrow (5-2) didn't allow a runner to reach third base until the ninth inning in the gem, during which he issued only one walk. It was his third career shutout and second of the season.
The Blue Jays right-hander tossed 76 of his 107 pitches for strikes and improved his ERA to 1.90, best in the American League, as Toronto clinched its three-game series at Rogers Center.
Kelly Johnson and Yunel Escobar each drove in fifth-inning runs off Jeremy Hefner (0-1) for the victors.
Mets starter Miguel Batista lasted only two innings before exiting with a sore back.
New York lost for the fourth time in five games.