Oakland has captured two of the first three in a four-game series, helping the A's start to recover from a stretch in which they lost six out of seven.
The game was deadlocked 3-3 heading into the eighth, but Toronto reliever Darren Oliver (3-3) gave up a one-out single to Josh Reddick and then walked Josh Donaldson. Oliver struck out Brandon Moss to give himself a chance to get out of the inning, but Callaspo doubled to left to bring home both runners.
Callaspo scored the third run of the inning on a single by Chris Young.
Ryan Cook (4-2) worked 1 1/3 innings of one-hit relief to get the win and Grant Balfour escaped trouble in the ninth to pick up his 30th save.
Balfour gave up an RBI double to Brett Lawrie and eventually loaded the bases with two outs before getting Jose Reyes on a grounder to second that ended the game.