The Jets, who dropped a 3-0 decision to the Seattle Kraken a night earlier rebounded with a decisive win.
Kyle Connor, Alex Iafallo, Jonathan Toews and Vladislav Namestnikov also scored for the Jets.
Josh Morrissey had three assists for the Jets.
Eric Comrie made 30 saves for Winnipeg, who moved to 6-2-0.
Dustin Wolf turned aside 27 shots for Calgary, who dropped to 1-7-1.
The Flames scored first on the power play 5:18 into the first when Morgan Frost hit Nazem Kadri with a cross ice pass which he one timed past Comrie, beating him glove side to make it 1-0.
The goal was his 1st of the season.
Kyle Connor tied the contest just over five minutes into the second period after Josh Morrissey hit him with a no-look pass the Jet winger snapped past Wolf.
Jonathan Toews masterfully redirected a feed from the corner from Josh Morrissey 6:24 into the second period to give the Jets the lead.
The goal was challenged by Calgary but was allowed to stand.
The goal was his 2nd of the season.
Gabriel Vilardi scored a power play to make it 3-1 Winnipeg at 9:50, lifting a short side backhand past Wolf off a feed from Mark Scheifele.
Mikael Backlund pulled the Flames to within a goal when Blake Coleman sent him in alone on Eric Comrie at 13:56.
The veteran centreman made short work of the Jets backup, beating him with a nifty deke to make it 3-2.
Alex Iafallo restored Winnipeg's two-goal cushion with a power play marker late in the period when Gabriel Vilardi worked the disc around Joel Hanley who was lying on the ice, before sliding the puck to Iafallo who snapped it just inside the right post at 18:50.
Blake Coleman made it 4-3 8:27 into the third period, converting a Mikael Backlund feed from the corner to score his 3rd goal of the season.
Vladislav Namestnikov scored an empty netter with 8 seconds remaining in regulation to seal the win for the Jets.
Calgary hosts the New York Rangers Sunday while Winnipeg hosts Utah.
SHOTS-CALGARY 33 WINNIPEG 32
ATTENDANCE-13,967
