Draisaitl made it 1-0 with a power-play goal at 3:12 of the first. He took a cross-ice pass from Connor McDavid and scored with a wrist shot from the right circle that went through the legs of both Predators forward Zachary L'Heureux and goalie Justus Annunen.
A little more than a minute later, Draisaitl left ice after taking a hit into the boards from Predators forward Ozzy Wiesblatt. Draisaitl would come back out for two more shifts later in the period, but he didn’t return to the bench for the start of the second.
McDavid had three assists, and Matt Savoie also scored for the Oilers (33-26-9), who had lost two in a row (0-1-1). Connor Ingram made 28 saves.
Fedor Svechkov scored for the Predators (29-28-9), who are 1-2-1 on a five-game road trip that will conclude at the Winnipeg Jets on Tuesday. Annunen made 27 saves.
Savoie pushed the lead to 2-0 at 2:32 of the second period, taking a pass from McDavid on a 2-on-1 rush and lifting the puck high over Annunen's glove as he slid across the crease.
Svechkov cut it to 2-1 at 4:52 of the third period with a shot from the high slot that deflected off the stick of Oilers forward Jack Roslovic and fluttered past Ingram's glove.
Hyman scored into an empty net with 1:07 remaining for the 3-1 final. The goal came moments after Steven Stamkos hit the post on a one-timer for the Predators.