Los Angeles moved within a game of the defending World Series champion Cardinals for the second wild card berth in the National League.
That advantage disappeared, however, when Cruz hit his homer in the sixth. Adrian Gonzalez expanded the Dodgers' cushion to 8-4 in the seventh with a two-run double.
The comeback made a winner out of reliever Shawn Tolleson (2-1), who walked one over 1 2/3 innings as the third of six Los Angeles pitchers.
Rookie Trevor Rosenthal (0-2) put two runners on in the sixth and became the losing pitcher when Edward Mujica gave up the home run by Cruz.