Morrow (3-1), in his sixth major league season and his third with the Blue Jays, faced only one batter over the minimum.
He gave up singles in both the first and fourth innings, but both those runners were erased in double plays. The third Los Angeles hit was a double by Mark Trumbo leading off the ninth, and he did not advance past second base.
Morrow struck out eight while throwing 102 pitches. His outing came one night after the Angels Jared Weaver threw the first no-hitter of his career.
Los Angeles had a three-game winning streak snapped and Toronto won its third in a row.
J.P. Arencibia put Toronto in front with a three-run homer in the third and the other two Toronto scores came when Trumbo made a throwing error at third base on a ground ball from Edwin Encarnacion.
The wild throw allowed Kelly Johnson to score from second and Yunel Escobar to come all the way around from first.
Dan Haren (1-2) gave up three earned runs on seven hits in seven innings to take the loss.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys