Viktor Arvidsson also scored in regulation for the Predators, who have won five of six.
Matt Hendricks and Milan Lucic had the goals for the Oilers, who got 42 saves from Cam Talbot.
Pekka Rinne stopped 30 shots for the win.
Nashville went up 2-1 seven minutes into the third when Ellis’ long knuckler beat Talbot up high after appearing to deflect off the glove of defender Brandon Davidson.
Edmonton tied it again on a power play with 4:29 left in the third. Leon Draisaitl sent the puck in front and Lucic tipped it past Rinne to end a 12-game scoring drought.