Dallas overcame a 3-1 deficit early in the third period on goals by Michael Ryder and Eric Nystrom, but Voynov scored on a slap shot and Dustin Brown added an empty-net goal with 27 seconds remaining.
Voynov scored in the second period on the power play to give the Kings their 3-1 advantage.
The Stars lost at home for the first time after opening the season with four home wins.
Jamie Quick made 30 saves to get the victory.
Kari Lehtonen suffered his first loss of the season following seven consecutive wins. He stopped 24-of-28 shots.
Los Angeles defeated Dallas for the second time in as many attempts this year, having posted a 1-0 victory last week.