The Kings let a 3-0 lead get away before taking advantage of a hooking penalty called on Ottawa's Clarke MacArthur with 1:32 to go in regulation.
That penalty was expiring as Carter tipped in a shot from Mike Richards. The Kings ended an early-season, two-game skid while Ottawa suffered its second straight overtime setback. The Senators have played all three of their games on the road this year.
Dustin Brown scored twice in the first period and Carter also tallied to give the Kings a three-goal cushion after the opening stanza. Two of those goals also came on the power play.
Notable deaths of 2014 [PHOTOS]