Edmonton improved to a perfect 4-0-0 on the young campaign and became the third team in NHL history to overcome a deficit to win each of their first four games in a season, joining the Los Angeles Kings in 1988-89 and Nashville Predators in 2005-06.
"We couldn't really find our A-game throughout the whole night, but those nights happen," said the shootout hero Draisaitl. "This league is too good to just be dominant and play perfect every game. It's great to see that we can find different ways to win games."
The Oilers found themselves shorthanded just 24 seconds into the game when Darnell Nurse was penalized for tripping. Thanks to back-to-back impressive Mikko Koskinen saves, however, they were able to kill it off and return to even strength.
New Jersey did eventually open the scoring 6:14 into the game as Kyle Palmieri tallied his second goal of the season. Oscar Klefbom had his point shot blocked in the offensive zone, sending the Devils in on a two-on-one rush with Palmieri calling his own number and beating Koskinen high glove side.
The Oilers didn't trail for very long, though, as Draisaitl delivered the equalizer at the 9:17 mark thanks to a brilliant display of passing that involved every position player on the ice.
Ethan Bear secured the puck in the Oilers zone, slid it up to Connor McDavid and the captain exploded into the neutral zone before dishing it over to Zack Kassian who was streaking down the right wing. Kassian entered the offensive zone and dropped it back to a pinching Nurse, who corralled the puck for a split-second and sent a perfect feed to the tape of Draisaitl on the left side for the one-timer redirect finish.
After lighting the lamp 50 times during the 2018-19 season, Draisaitl had his second marker of the season and eighth point, while Kassian and Nurse each got their fourth point with the helpers on the 1-1 goal.
The teams exchanged opportunities in a fairly wide open middle frame but both Koskinen and Devils netminder MacKenzie Blackwood held their ground until the 14:12 mark when Nikita Gusev stepped into a slap shot that went high blocker side to give New Jersey a 2-1 lead.
James Neal, who lit the lamp four times two nights earlier against the New York Islanders, was held at bay by the Devils for almost two periods until he picked up his NHL-best seventh tally of the season with just 28 seconds to go in the second period.
With the Oilers on the power play, Ryan Nugent-Hopkins fired a shot on net from the high slot and Neal managed to get his stick on it to fool Blackwood and make it a 2-2 game. Shockingly, considering how consistently involved he is in the Oilers offence, the setup was Nugent-Hopkins' first point of the season, while McDavid got the second assist for his team-leading ninth point.
With his seventh goal in just four games, Neal set a new franchise record, beating out Wayne Gretzky who scored six in 1983-84 and Glenn Anderson who also tallied a half dozen in 1987-88.
"I'm just having fun again playing the game," Neal said of his historic start. "We're sticking together, we're becoming a team really quickly and having a lot of fun doing that.
"I'm in a great spot. I've got a great opportunity here and I'm just trying to take advantage of it."
Damon Severson put the Devils ahead 3-2 with 4:25 remaining in the third period, one-timing a pass from Taylor Hall with Palmieri screening Koskinen in front. Edmonton's coaching staff spent some time examining the replay and debating a challenge for goaltender interference but ultimately opted to bite the bullett and play on.
The Oilers pulled Koskinen in favour of an extra attacker with 1:31 to go and McDavid drew a penalty just 15 seconds later, sending the visitors to a crucial six-on-four power play.
Just 10 seconds into the man advantage, McDavid snagged a loose puck out of the crease and deposited the 3-3 goal for his third of the season and team-leading 10th point. The captain has now scored at least one goal against every opposing team in the NHL.
An action-packed overtime period solved nothing as the game advanced to the breakaway competition where the Deutschland Dangler was the sixth and final shooter and the only one to score, giving Edmonton its fourth consecutive victory.
"Winning makes everything easier and better, but we're working for it," Draisaitl said. "We're playing the right way, we're working hard for our wins and it's great to see different guys contribute and make a difference every night."
Special teams turned out to be pivotal on Thursday as the Oilers converted twice on the PP and killed off both penalties they took.
"We looked a little sluggish out there, but I liked the way we hung around and battled," said Head Coach Dave Tippett. "Special teams ended up being the difference in the game. Our PK was pretty good and our PP got us a couple of big goals. They can't all be masterpieces so we'll take the win and move on."
Koskinen finished the night with 28 saves combined in regulation and OT, but his most impressive denial came in the shootout when he extended his lengthy right leg to deny 2019 first-overall pick Jack Hughes on the forehand deke.
"That felt pretty bad after the stretch but I'm happy that I stopped it," the big Finn laughed.