LaCombe's assist gave the newly 24-year-old defenseman points in eight of his last 10 outings. LaCombe leads Ducks blueliners in points, goals and assists this season.
Carolina appeared to get back within one later in the third period on a rebound by center Sebastian Aho, but the goal was wiped out by an Anaheim challenge for goaltender interference.
The Canes would strike for real on the next shift though on a tic-tac-toe passing play, with Aho sliding a perfect backdoor pass to Svechnikov for a tap-in goal. The goal extended Svechnikov's point streak to five games.
Anaheim would then preserve that 2-1 advantage until the final 60 seconds of regulation, but could not hold off a final Carolina push as Jarvis found free space in the low slot and lifted a wrister over Dostal's glove off a setup feed from Martin Necas. With two helpers on the night, Necas moved into a tie for ninth in the NHL in assists this season.
Gauthier then ended the festivities on his first shift of overtime, using his trademark shot off the rush to clinch a cathartic win for Anaheim.