Calgary held a 10-8 edge in shots on goal through 20 minutes.
The score remained 2-2 when the second period was through, with both Dustin Wolf and Hellebuyck showcasing their skills with second-period stops.
Hellebuyck turned away a series of shots from Jakob Pelletier and Frk, while Wolf's best save of the middle frame came in the form of a stretching, right pad stop on an Adam Lowry partial break.
Wolf was tested again early in the third on a Winnipeg powerplay, but stood tall making three key saves, including a back-door blocker-hand robbery on Mark Scheifele.
But Niederreiter put Winnipeg ahead at the 6:28 mark, jamming home his second goal of the game on a rebound in front of the Calgary cage.
Simon Lundmark and Kyle Connor added insurance markers for the home side in the final minutes of the third period.
The Jets outshot the Flames 27-18.
Calgary went 0-2 on the powerplay, while Winnipeg finished 1-3.