Ryan Nugent-Hopkins scored the tiebreaker with 5:16 remaining and assisted on both of Draisaitl's goals as the Oilers snapped a two-game skid.
Draisaitl surpassed 100 points on the season with his performance.
"Obviously I'm excited about it," Draisaitl said of being the first player in the NHL to hit the century mark this season. "It's a special milestone for me, but that's over now, now it's about making the playoffs."
"It's outstanding how fast he reached it this year," Nugent-Hopkins said of Draisaitl eclipsing the 100-point plateau. "It's pretty crazy. His offense is obvious, how good he is at making plays, but his defense over the last stretch has been so solid, too. Inside he's pretty proud. He should be. It's a huge milestone."
"It doesn't matter how you play, you've got to get results this time of year," Winnipeg's Blake Wheeler said. "We're in a position where we're tied with five minutes left in the game, we can't leave with zero. You just can't do it."
Draisaitl became the first German-born player and seventh player in Oilers franchise history to hit the century mark in consecutive seasons.
"He is just a beast out there, in all situations too, its not just power play, it's penalty kill and face-offs," Oilers head coach Dave Tippett said. "He is playing really well right now."
The Jets controlled the pace in the second period and were rewarded 13 minutes in when Shaw was sprung on a breakaway and beat Oilers goalie Mike Smith.
Just 44 seconds later, Blake Wheeler made a nice move to set up Connor for his 33rd goal of the season and 100th of his career.
Draisaitl deflected home a shot by McDavid on a power play with 13 seconds left in the second period to tie it up 2-all.
The Oilers surged back in front with five minutes to play in the third as Draisaitl fed Nugent-Hopkins and he picked the corner for his 19th.
Winnipeg had intense pressure with their goalie pulled for the final couple minutes, but Smith was solid to preserve the win, finishing with 38 saves.
Defenseman Kris Russell returned to Edmonton's lineup after a lengthy absence with a concussion and forward Zack Kassian came back from serving a seven-game suspension. In addition, forward Kailer Yamamoto is back skating with the team and is expected to return from an ankle injury shortly. ... Still out with injuries for Edmonton were Oscar Klefbom (shoulder), Joakim Nygard (hand), James Neal (ankle) and Mike Green (knee). ... The Jets are even more banged up, missing Patrik Laine (lower body), Josh Morrissey (upper body), Bryan Little (upper body), Carl Dahlstrom (upper body), Adam Lowry (upper body), Mathieu Perreault (upper body), Luca Sbisa (upper body), Sami Niku (lower body) and Mark Letestu (upper body).
Jets: Host Buffalo Sabres on Tuesday.
Oilers: At Nashville on Monday.
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