Ethan Bear registered his first career National Hockey League point with a secondary assist on McDavid's game-tying goal.
Talbot made 30 saves on 31 shots to end the night with a .968 save percentage. He improved to 24-26-2 this season.
"He was a calming influence," said Oilers Head Coach Todd McLellan of Talbot. "He managed the game well. We hope that he can work on his game from now until the end (of the season)."
McDavid finished with a game-high nine shots on goal, edging runner-up Tavares by three. The Oilers Captain saw 27:27 of ice time and set a career-high in goals by tallying his 31st of the campaign.
"He just takes over the game when he wants to," Talbot said of his captain McDavid. "He has that ability on any given night. In one-goal games, that's who you want on the ice... He never ceases to amaze."
Neither side could find the back of the net through 40 minutes. The deadlock broke at 1:54 of the third when Thomas Hickey roofed a backhander past Talbot.
McDavid evened it up with 1:50 remaining in the game, getting a fortunate bounce off former Oiler Brandon Davidson's stick to knot it up 1-1.
"You become a fan when you're sitting on the bench," said Jujhar Khaira of McDavid. "He took over the game every time he had the puck."
McLellan had high praise for his captain post-game.
"That's remarkable that an individual can play like that," he said. "It speaks of his skating ability and how efficient he is."
The Oilers best chance of the opening period came courtesy of Ryan Strome, who rattled iron after cutting into the middle of the Isles' zone and releasing a wrister far side on netminder Christopher Gibson.
Khaira - who dropped the mitts with New York enforcer Cal Clutterbuck in the first - later centred a feed for Iiro Pakarinen that the forward couldn't grasp.
"It's one of those things where this team is my family and the way I was raised, you always stick up for your family," said Khaira of the scrap with Clutterbuck. "If I can help out, I will."
At the other end of the ice, Talbot ate Tavares' quick wrister and stopped a bullet from defender Ryan Pulock. The Oilers keeper stopped all nine shots he faced in the opening 20.
Midway through the first period, the Oilers organization welcomed back Jordan Eberle with a tribute video. The right winger spent seven seasons with the Oilers, compiling 165 goals, 217 assists and 382 points in 507 career games.
The goose eggs remained intact through two periods, as neither side could light the lamp - despite the Oilers storming out with some gusto in the middle frame. The Orange & Blue threw four early shots at Gibson, including one off the rush by McDavid and ended the period with 15 shots total.
"I thought we did a good job overall during the game to play a tight-checking game and take our chances when we had them," said McDavid.
But it was the visitors who got an early third-period marker to open the scoring.
After the Oilers failed to clear their zone, rearguard Hickey got the puck and navigated down to the goal-line, shifting to his backhand and lifting the puck under the bar to open the scoring less than two minutes into the final frame.
McDavid tied the game up with under two minutes to play. The Oilers Captain sifted the puck at the net from under the goal-line, getting a fortunate bounce off Davidson's stick. Rookie defenceman Bear registered an assist on the goal to record his first career NHL point.
"I thought the guys battled hard," said McDavid. "We found a way to get a goal - albeit a little cheeky - and get the win."
It was an eventful overtime period, with chances from both sides. Gibson robbed Oscar Klefbom then stopped McDavid on a solo effort; McDavid was awarded a penalty shot after being hooked by Mathew Barzal on a breakaway; and Talbot thwarted Eberle on the goalmouth, forcing the game to be decided by a shootout.
"Leddy made a nice play to Ebs there... I just got my pad across for a desperation save," said Talbot of the stop on Eberle.
Ryan Nugent-Hopkins and McDavid scored in the shootout, while Talbot stopped Tavares to give the Oilers the come-from-behind victory.
Edmonton concludes their five-game home stand Saturday against the Minnesota Wild.