Draisaitl gave Edmonton a 1-0 lead when he scored shorthanded at 5:12 of the second period. He stole the puck from Nylander at the side of the net and shot between Andersen's pads from the goal line.
Brooks tied it 1-1 with his first NHL goal on the same power play 43 seconds later when he deflected a shot in the slot from Jason Spezza. Brooks was making his season debut after playing seven games last season.
"It's nice for it to come from a guy like Spezza," the 24-year-old said. "I played with him my first NHL game ever (Dec. 28, 2019) and I got him to sign a stick for me, so to say he assisted on my first goal, a guy that's played for that long at that caliber, it's a pretty cool moment for me."
Marner scored into an empty net with one second left in the third period to make it 4-2.
"The (second and third) goals were mistakes by us, poor giveaways in our own end and we didn't get in a lane, and taking a penalty in the third and it cost us the game," Oilers coach Dave Tippett said.
NOTES: Oilers forward James Neal played 10:37, had three shots on goal and was minus-2 in his season debut. He was removed from the NHL COVID-19 protocol list on Jan. 15. ... Andersen got his 139th win with the Maple Leafs, passing Curtis Joseph for fourth in Toronto history. "It's obviously cool to be mentioned in the same sentence as a guy like 'Cujo'," Andersen said. "He's a phenomenal person. He's one of the greats in Toronto, and it's special, but when you're a part of a great team, you're going to end up with some wins. I'm happy about the way we responded tonight." Andersen is 139-68-33 with Toronto; Joseph was 138-97-28. Turk Broda holds the Toronto record at 304-222-102 (ties). ... Brooks played seven NHL games last season.