Nino Niederreiter made it 2-0 at 16:15, burying a rebound in front after Wheeler's initial redirection was stopped by Vanecek.
Morgan Barron scored five-hole on a penalty shot to extend the lead to 3-0 at 2:42 of the second period.
"He only brings it out against opposing goalies," Hellebuyck joked about Barron's move. "No, that was a beautiful move, and he earned it."
Kyle Connor made it 4-0 at 10:34, scoring under Vanecek's right arm from the right hash marks for his 30th of the season.
"No one really had a good night, unfortunately," Devils defenseman Damon Severson said. "It just was one of those nights where it didn't go our way at all. We had a decent first period, but overall, it wasn't our night for sure."
Dubois pushed it to 5-0 at 10:19 of the third period with a one-timer from the right face-off dot, and Ehlers scored with a one-timer from the left circle on a power play to make it 6-0 at 14:10.
"Eventually, if you keep doing the good things and playing the right way and creating offense, it's going to go in for you," Winnipeg coach Rick Bowness said. "Now, back-to-back six goal games (Winnipeg won 6-2 against the Detroit Red Wings on Friday), that's rare for us, but it's really good to see. Give the guys credit, they stayed in the fight and they just kept putting pucks on the net and making plays, and finally it's going in."
Hischier ended Hellebuyck's shutout bid with 14 seconds remaining for the 6-1 final.
"They wanted it more," Hischier said. "I think they just outbattled us tonight, but I also think the score was a little too high. We had our chances for sure, but if you give up six goals you're not winning a hockey game, so we've got to clean that up."