Shattenkirk, Troy Terry, Cam Fowler and Isac Lundestrom scored for Anaheim.
The game remained scoreless through the opening 20 minutes thanks to a sterling performance by Gibson, who turned aside 18 Kings shots in the first period.
Ryan Getzlaf left the game in the initial period after an awkward collision along the boards and did not return. Getzlaf leads the Ducks in assists (19) and ranks second in points (1-19=20).
Anaheim picked up the pace early in the middle frame, with several quality scoring chances early in the period, but Kings netminder Jonathan Quick matched Gibson, keeping the Ducks from taking the night's first lead.
The Ducks finally broke through midway through the second. After an unsuccessful Anaheim power play, Terry grabbed a loose puck in the corner and worked his way to the slot, lifting a shot over Quick's shoulder to put Anaheim ahead.