In the lone Thanksgiving fixture, the Predators were kept scoreless in 60 minutes of regulation time for just the second time this season but they managed to snatch two points courtesy of Filip Forsberg's OT goal.
Forsberg was assisted by Roman Josi and Shea Weber with just over one minute of the additional period to play at Bridgestone Arena.
The Predators have not won in regulation since scoring nine goals against the Toronto Maple Leafs on November 18.
But they have scraped through to victory via two shoot-outs and an overtime result to move two points clear of the Western Conference's Central division.
The Oilers, meanwhile, slumped to their eighth consecutive defeat as they remain six points clear bottom of the West's Pacific standings.