Talbot, who bailed the Oilers out while they were outshot 13-2 in the third period, knew they would have a chance to win if he could simply get them to the 3-on-3 overtime.
McDavid won it when he one-timed Draisaitl's feed past Thomas Greiss for his sixth goal of the season.
"They're an extremely good home team," Talbot said. "We figured they would come out and give us their best in the third period. We were able to weather the storm. Our two big guns took it down the ice and got us a win tonight. That's what we look to them for in situations like that, and we got it tonight."
Jordan Eberle scored for New York (8-5-2), which hasn't lost in regulation at home this season (5-0-2). Greiss made 23 saves.
"We fought hard all game and gave ourselves an opportunity to win, so we'll build on that," Islanders captain John Tavares said.
Draisaitl gave the Oilers a 1-0 lead at 1:59 of the second period when he skated in alone after Jason Chimera was stripped of the puck at the blue line. He put a soft slap shot between Greiss' skates for his fourth goal of the season.
The Islanders tied it 1-1 at 4:43 of the second on Eberle's fifth goal. Eberle, who was traded from Edmonton to New York for Ryan Strome on June 22 after six seasons with the Oilers, took a pass from Mathew Barzal and sent a wrist shot from the right circle past Talbot.
"It was really weird," Eberle said of playing against the Oilers. "First period, something you can't prepare yourself for. As the game went on, I settled in and started to play. I didn't know what to expect. It's weird when you see that. Your mind starts to settle in after the first or first [few] shifts and it's another hockey game, and you compete."
