Los Angeles' fourth victory in five games came in the second outing of a 10-game road trip. The Kings will not play another home game until Feb. 24.
Magnus Paajarvi gave Edmonton the lead 3:21 into the second period but Smyth scored 24 seconds later while Dustin Penner was in the penalty box for elbowing. Smyth's second goal came after Theo Peckham was called for hooking.
Jack Johnson assisted on both of Smyth's goals and added a third-period score of his own.
The win went to Jonathan Quick, who made 32 saves.
Nikolai Khabibulin stopped 23 shots for Edmonton, which has lost seven out of eight.