Edmonton outshot Winnipeg 20-11 in the first period.
"The big concern is where we are with the mental state," Oilers coach Todd McLellan said. "We're not near competitive enough. We're not outworking teams. It feels like it in moments of the game, but consistently from minutes 1 to 60 the last two games we haven't come close to outworking teams, and structurally, we're about as loose as we can be. We're missing assignments."
Draisaitl scored at 12:53 of the second period to make it 2-1 on a pass from Connor McDavid.
Nugent-Hopkins tied it 2-2 40 seconds later, splitting the Jets defense and lifting a shot over Hellebuyck.
Ehlers scored 1:09 apart in the second to restore the Jets' two-goal lead. He kept the puck on a 3-on-2 rush and picked the corner on Talbot at 16:48 to make it 3-2. He scored again at 17:57 to put Winnipeg up 4-2.
"We do still have a young team and guys have to build confidence in themselves and respect the fact that the opposition has good players and bad things are going to happen," Wheeler said. "But all we can do is get back to our game and have confidence that we can prevail in the end."