An inning after Toronto stranded two men in scoring position, McCoy reached on an error from Eric Aybar to begin the 10th. An Eric Thames single moved him to second and he took third on a fielder's choice.
With runners on the corners, the Angels went with a five-man infield, bringing in Torii Hunter from right field. Adam Lind then hit a grounder to Hunter and McCoy beat his throw home to give the Blue Jays their sixth win in eight games.
"There are things on the defensive side that definitely swung the momentum of the game," Angels manager Mike Scioscia said.
Jerome Williams allowed a pair of unearned runs as a result of his throwing error in 6 1/3 frames for Los Angeles.
The loss dropped the Angels five games behind the AL West-leading Texas Rangers, who were idle on Monday. They are also 4 1/2 games back of Boston in the wild card race.
Down a run, Toronto grabbed the lead in the fourth. Edwin Encarnacion led off with a walk and Kelly Johnson hit a chopper that Williams barehanded. However, his throw to second base was off-line. After Brett Lawrie walked to loaded the bases, Colby Rasmus grounded into a 3-2-3 double play. J.P. Arencibia then delivered a two-run single to right field.
Thames had three of Toronto's nine hits...The Blue Jays finished 1-for-11 with runners in scoring position...Hunter clubbed his 21st home run of the season and Trumbo upped his home run total this year to 28.