Handzus scored the only goal in the shootout period and Anze Kopitar and Alexander Frolov scored in regulation to give the Kings their fourth consecutive victory.
Jonathan Quick made 25 saves for the Kings. He also frustrated Dallas in the shootout although he appeared to allow a goal to Mike Ribeiro in the fourth round. The goal was disallowed after a video review showed the puck went in off Ribeiro's skate.
Mike Modano and James Neal scored in regulation for the Stars. Alex Auld recorded 25 saves.
Modano's goal at 7:07 of the second period put Dallas ahead 2-1. But Kopitar tallied with 8 seconds to play in the period to tie it.
Dallas threw seven unsuccessful shots at Quick in the third period. Auld made three saves.