The Tigers missed a chance to move into a tie for the lead in the American League Central, remaining a game behind the Chicago White Sox.
Home runs by Prince Fielder in the second and Alex Avila in the third allowed Detroit to rally from an early 2-0 deficit, but there was no scoring after that until Callaspo delivered his game-winning hit.
Kendrys Morales reached on a one-out single in the ninth off Octavio Dotel (5-3) and gave way to Bourjos as a pinch runner.
Ernesto Frieri (4-0) worked the top of the ninth to get the win.
Notable deaths of 2014 [PHOTOS]