Mark Scheifele scored both of Winnipeg's goals, including an empty-net tally with 11 seconds to play as the Jets built a 3-1 lead in the best-of-seven series.
Minnesota goalie Devan Dubnyk made 26 saves.
Game 5 is Friday night in Winnipeg, where the Jets dominated at times in the first two games.
Hellebuyck made 11 saves in the first period, 10 in the second and nine in the third.
Scheifele's first goal came with 28 seconds left in the first period after the Jets killed off the first Minnesota power play of the game. It was his second goal of the series.
Kyle Connor and Josh Morrissey assisted on Scheifele's first goal, which allowed Winnipeg to hold a 1-0 edge in all four games of the series.
Winnipeg scored first-period goals in both road games in the series after neither team posted a goal in the opening period of the first two games.
Hellebuyck was responsible for Minnesota's second power play after he was called for slashing midway through the second period.
Yet earlier in the period it was Hellebuyck's pad save of defenseman Matt Dumba's shot that kept the blanking in place.
The Wild applied pressure in the third period, with six of the first seven shots on goal across 11 minutes. Yet the Jets perked up for a stretch and registered six consecutive shots on goal, causing Minnesota to scramble a bit.
This game was in stark contrast to an offensive-flowing Game 3 when the teams combined for eight goals as the Wild won for the only time in the series. That 6-2 outcome threatened to shift the momentum of the series, particularly with Hellebuyck pulled after two periods.
The Jets made a lineup change Tuesday with defenseman Tucker Poolman drawing an assignment for his Stanley Cup playoffs debut. Defenseman Tyler Myers was out of the Winnipeg lineup after sustaining an injury late in Game 3.
--Field Level Media
Winnipeg | Minnesota | |
Mark Scheifele 2 | Points | N/A |
Mark Scheifele 2 | Goals | N/A |
Kyle Connor 1 | Assists | N/A |
N/A | Power Play Goals | N/A |
N/A | Short Handed Goals | N/A |
Connor Hellebuyck 1.000 | Save Percentage | Devan Dubnyk .963 |
Connor Hellebuyck 30 | Saves | Devan Dubnyk 26 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Winnipeg | 28 | 2 | 0-1 | 2-2 | 4 | 28 |
Minnesota | 30 | 0 | 0-2 | 1-1 | 2 | 26 |