The Dodgers trailed 4-1 heading into the seventh but six of their eight hitters reached base against reliever Neil Ramirez with five hits and an error.
Cubs rookie second baseman Logan Watkins couldn't handle Juan Uribe's hard-hit grounder with one out. That allowed the first run of the rally to score on a fielder's choice. Los Angeles scored all the runs in the inning against Ramirez (2-3), but only one was earned.
The Dodgers moved 2 1-2 games ahead of idle San Francisco in the NL West race.
Los Angeles overcame a shaky start by Zack Greinke, who allowed four runs in five innings.
