Mark Giordano made it 2-0 with a slap shot from the point that deflected off Mason Appleton for a power-play goal at 19:14.
The Flames outshot the Jets 16-7 in the first period.
"We're fighting for our season," Calgary forward Johnny Gaudreau said. "Every game's important; we can't afford to lose any games. We take it one game at a time, but looking at the standings, we can't afford to lose. It's nice to get a win."
Appleton's shot from the high slot deflected off Flames forward Milan Lucic and past Rittich 34 seconds into the second period to cut it to 2-1.
Stanley tied it 2-2 at 6:19 when he took a pass from Kyle Connor and shot over Rittich's shoulder from the right circle.
The 6-foot-7 defenseman was a first-round pick (No. 18) by Winnipeg at the 2016 NHL Draft. The goal came in his 23rd game with the Jets.
"It's a pretty good feeling to get that one," Stanley said. "It's something you dream of as a kid, playing your first NHL game, and scoring a goal in the NHL. That was pretty cool. I would've liked a better result for the team, but we'll come back Monday with another good game."
NOTES: Gaudreau had an assist in his 500th NHL game. ... Jets defenseman Dylan DeMelo played his 300th NHL game. ... Calgary defenseman
Michael Stone
had two shots and was plus-1 in 13:55 of ice time in his first NHL game since Feb. 25, 2020.