O'Sullivan scored in the third round of the shootout and Horcoff added the decisive goal in the next round after Dallas captain Brendon Morrow hit the post on his try.
Lubomir Visnovsky and Ladislav Smid scored in regulation for the Oilers. Smid's goal with 3:07 to play in regulation tied the game 2-2 and forced overtime.
Jeff Deslauriers made 33 saves in goal for Edmonton while Nikolai Khabibulin remained sidelined with an injured back.
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Megyn Kelly: Santa Claus and Jesus are both white men