Laine now has a team-leading 15 goals, but that was as close as they would come.
Draisaitl and Benoit Pouliot scored 20 seconds apart midway through to ice a lopsided final.
"We cut it to a goal in the third and they bounced back and got two more. It's kind of deflating," Wheeler said. "You get a little momentum, and (if) it (stays) a one-goal game for most of that third period, I think we like our chances with everything that happened throughout the game."
With the Jets on top entering the second period, the Oilers quickly tied the game before taking their first lead with their second and third power-play goals of the night, five minutes in.
Draisaitl struck first, jumping on a loose puck in the blue paint and plunging it past Hellebuyck only 51 seconds in. Then, Letestu drove hard to the net and buried a feed from Milan Lucic to give the visitors a 3-2 lead at 5:06, punishing the Jets for yet another undisciplined penalty.
After the Jets worked their way back into it with a couple of strong shifts in the offensive zone, the Oilers took a 4-2 lead on a fortuitous bounce at 11:43.
Pat Maroon took the shot from a sharp angle, and after first hitting Paul Postma at the side of the net, the puck banked in off Hellebuyck as he contended with the 6-foot-3, 215-pound Zack Kassian in front.
"We took some not-so-smart penalties," Laine said. "That's not the way we wanted to play, but that kind of stuff happens and we have to deal with it. But it wasn't our best game tonight. … They have a good team and they were just better than us today."
The Jets opened the scoring just 35 seconds in as Little, Blake Wheeler and Drew Stafford went head-to-head with Connor McDavid off the opening faceoff. With the Oilers on their heels in their end own, Wheeler found Little wide open out front, and No. 18 made no mistake, firing a shot high over Cam Talbot for his first of the year.
Letestu replied with a power-play goal for the Oilers at 2:31, tying the game at one. Leon Draisaitl made a great slap pass to the high slot, where Letestu made contact, sending it high over the glove for his third of the year.
A blistering shot by Laine put the Jets went back in front on their first power play of the game at 10:14. Toby Enstrom put the puck on a tee and Laine, with a clear lane from well out at the left point, drove it clean past Talbot.