With the Kings trailing 2-1 in the final minute of the third period, Los Angeles pulled goalie Jonathan Quick to add an extra attacker and Voynov notched the equalizer with a blast from the left point with 44 seconds left.
After a scoreless overtime, the game went to a shootout. Following two scoreless rounds, Carter beat Roberto Luongo with a quick backhander and Quick then stopped Zack Kassian to seal the victory.
Carter also scored in regulation while Quick finished with 21 saves for the Kings, who took their second straight after starting the season at 0-2-1.
Kassian and Alexandre Burrows scored and Luongo turned aside 26 shots for the Canucks, who fell for the second time in two nights.