The Yankees had forced extra frames on Derek Jeter's lead-off homer in the bottom of the ninth, but their defense let them down two innings later.
McCoy came in as a pinch-runner and drew a throw from Lowe that got past first baseman Eric Chavez, allowing him to advance to third.
Adeiny Hechavarria then hit a dribbler to third baseman Jayson Nix and McCoy took off for the plate. After recording the out at first, Chavez fired to home plate but it was too late catch McCoy.
The tally made a winner of Darren Oliver (3-2), who hurled two scoreless frames as the Blue Jays took the first of a three-game set.