The Flames claimed victory, and a 2-1 lead in the best-of-five series, after three power-play goals finally broke Winnipeg's resistance.
The Jets took the lead through Denmark forward Nikolaj Ehlers in the first period before Swedish international Elias Lindholm levelled for Calgary shortly afterward.
Calgary goaltender Cam Talbot made 33 saves for the Flames while Jets counterpart Connor Hellebuyck made 26 saves.
The Flames can assure themselves of a place in the playoffs with victory in game four, which takes place in Edmonton on Thursday.
The New York Islanders meanwhile are also one win away from the playoffs after defeating the Florida Panthers 4-2 in Toronto on Tuesday.
Jordan Eberle scored twice and Semyon Varlamov made 26 save as the Islanders moved into a 2-0 series lead in the Eastern Conference clash.
"I liked our resiliency," Islanders coach Barry Trotz said. "We'll have to do it again. Plain and simple. That's where we're at.
"When all else fails, we've been desperate and committed to block a shot if we've needed to. Box out around the net.
"All those types of things where those are the details and little things that help you win."
Game three in the series takes place Wednesday.