Ryan Johansen made it 5-2 on the power play at 9:28, redirecting a pass from Josi.
Forsberg scored at 4:51 of the third period to cut it to 5-3, one-timing a cross-ice pass from Duchene.
"After we scored they came back and got those three quick ones and turned the game around," Saros said. "We tried to get back, but it wasn't enough today. Then when you get close, you can't give up that next one, that's kind of how it was tonight."
Draisaitl scored on the power play at 8:55, converting a centering pass from Ryan Nugent-Hopkins to make it 6-3.
"At 5-3, that penalty would have been nice to kill off, but it's hard, they have five elite players out there; two of the best in the world and the other ones aren't too bad either on that unit," Forsberg said. "I thought the killers did a great job all night, but you can't stop them when you're taking that many penalties. That was something that we kind of shot ourselves in the foot with on the comeback."
Nino Niederreiter scored on a 6-on-4 power play with Saros on the bench for an extra skater to make it 6-4 at 17:10, and Kane scored into an empty net at 18:23 for the 7-4 final.
"I think if you look at the goals we gave up, there were a few things we can do better," Oilers coach Jay Woodcroft said. "One of them was a 6-on-4, but there are things we can do better. But I keep going back to the fact the team is 7-3, but we realize we're not perfect, we have areas that we need to get better in and [penalty kill] is certainly one of them."
NOTES: n 21 games against the Predators, Draisaitl has 30 points (20 goals, 10 assists). He has five five-point games, which is fifth among active players behind Evgeni Malkin (eight), McDavid (seven), Sidney Crosby (six), and Brad Marchand (six). … McDavid has five multipoint games through the first 10 games of the season. … Kane has five NHL hat tricks. … Duchene had his 400th NHL assist.