Hellebuyck didn't see a shot for nearly the entire first half of the opening period but when called upon was brilliant for the remaining 50 minutes.
"Bucky held us in there. They had some sustained pressure but Bucky was just able to smother it to get a whistle for us," said Mark Scheifele who ended up with the game-winning goal.
"He definitely was the biggest reason we won tonight."
Kyle Connor registered his second consecutive multi-point game and has four points (2-2) on the road trip so far. With the win, the Jets have four straight victories and improved to 44-25-4.
"We had really good sticks and knocked an awful lot down. We made some blocks but it was hard for both teams to get a handle on the puck," said Paul Maurice.
"The defensive sticks were good, disrupted a lot of plays which prevented them from getting to the net but when they did Connor was right on them."
Winnipeg used a power play to get on the board first at 15:56 of the opening period. Connor got the first chance after Jacob Trouba's point shot rebounded off the end boards, but the puck trickled to Scheifele at the top of the crease. The Jets' alternate captain lifted the puck over John Gibson and in for his 35th of the season.