Bo Horvat scored for the Islanders (29-28-8), who have been outscored 10-3 in their past three games (0-2-1).
Sorokin, who finished with 33 saves, kept the game scoreless at 15:36 of the first period when he got a piece of Connor Brown’s short-handed breakaway attempt with his glove.
The Oilers outshot the Islanders 17-6 in the opening frame.
“In the first, Ilya kept us in the game,” New York coach Patrick Roy said. “He was really good. We gave up too many chances. I wasn't surprised. They played last night. We were coming back from the West Coast. In my days in Montreal, it was always tough that first game back, so I was very happy with the way we bounced back in that second period. And in the third period, I thought we did a lot of good things, and I was pretty proud of our group.”
Draisaitl gave Edmonton a 1-0 lead at 8:46 of the second period. He took a pass from Brown as he entered the offensive zone and skated into the top of the left circle before beating Sorokin under his glove with a slap shot.
Horvat tied the game 1-1 at 1:21 of the third period, beating Pickard blocker side from the right circle after electing to shoot on a 2-on-1 rush.
Anthony Duclair had a chance a short time later to give New York the lead, but he missed the net with a backhand move on a breakaway at 4:38.
“It was good to come back and get that point there,” Horvat said. “They played a pretty solid game themselves, and we fell short. We had a couple semi-breakaways, a couple nice moves around tight in front. ... We just have to cash in on those, find ways to bury those. Obviously, we’ve had trouble putting the puck in the net the last three games, and we have to find a way.”
Casey Cizikas also had a good chance to win it for New York in overtime, but his shot from below the left circle went above the crossbar at 2:52.
“We've been through a lot,” Pickard said. “I mean, I've only been here since the start of last year, but there's obviously always a ton of adversity. So, we're no strangers to it. We've been putting together some pretty good efforts, we just haven't been able to score and have been running into some hot goalies, and (we) did that again tonight. It almost took 65 minutes to score two. So, credit to our team. We defended really well, we played the right way, and we got the reward we deserved.”
NOTES: Oilers forward Connor McDavid had the primary assist on Draisaitl's overtime goal to extend his point streak to 10 games (two goals, 12 assists). ... Draisaitl is one goal away from scoring 50 for the fourth time in the past seven seasons.
