Haren yielded seven singles, walked one and struck out one.
Noel Cuevas hit a three-run homer in the ninth and Scott Van Slyke a two-run drive in the eighth.
Justin Maxwell went 3 for 5 for the Royals, including a two-run single in the eighth.
Royals left-hander Jason Vargas allowed a run on four hits in four innings, the first run off him in nine innings over three starts.
The Dodgers loaded the bases in the fourth off Vargas, but came away empty when A.J. Ellis hit a flyball to center field to end the threat.