McDavid intercepted an off-target pass by John Tavares to start a 2-on-1. McDavid carried the puck into the New York end of the ice dropping the puck to Draisaitl, who flipped a behind-the-back pass to McDavid at the circle to set up a one-timer.
The goal was the sixth of the year for McDavid.
"Our two big guns took it down the ice and got us a win," said Cam Talbot, who made 36 saves. "That's what we look to them for in situations like that, and we got it tonight."
Draisaitl also scored for Edmonton, which has won two of three to improve to 5-8-1.
"When you have the record we have right now, the right note's winning all of them," Edmonton coach Todd McLellan said.
The Islanders didn't come out too disappointed, either, despite losing two of three and falling to 8-5-2. New York is 5-0-2 at Barclays Center this season.
"I knew it was going to be a tough game," New York coach Doug Weight said. "They played one of their better games. We did as well."
Thomas Greiss made 23 saves, and the Islanders got their goal from former Oiler Jordan Eberle. The first of two regular-season meetings between the teams also marked the first matchup since Edmonton traded Eberle to New York in June for Ryan Strome.
"It was really weird," Eberle said. "As the game went on I settled in and started to play. I didn't know what to expect. ... Your mind starts to settle in after the first (period)."
Each goalie made 17 saves before Draisaitl broke through to make it 1-0 1:59 into the second period. It was Draisaitl's fourth goal of the season.
Eberle scored 2:44 later, snapping a shot from the right circle over Talbot's glove.
Both teams tightened up defensively after that, although there were some scoring chances. McDavid had a short-handed semi-breakaway late in the second period, but New York defenseman Ryan Pulock's effort took away shooting options from the reigning Hart Trophy and Ted Lindsay Award winner. Early in the third, Zack Kassian couldn't convert a side-of-the-goal shot attempt as Greiss came out to challenge.
New York RW Josh Bailey's nine-game point streak ended. Bailey leads the Islanders with 15 assists and 18 points. ... During the third period, New York announced LW Nikolay Kulemin would not return after suffering an upper body injury. He had been boarded by defenseman Eric Gryba in the second period.
Oilers: Continue four-game East Coast trip Thursday night in New Jersey.
Islanders: Begin a two-game road trip Friday night in Dallas.
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