The Flames finished the season 3-5-1 against their Northern Rivals.
With the victory, the Jets snapped a franchise record seven-game losing streak.
Calgary's special teams had a tough outing, going 0-5 on the powerplay and allowing a short-handed goal and a powerplay marker.
Jacob Markstrom made 15 saves between the pipes for the Flames, while Connor Hellebuyck turned aside 32 shots for the Jets.
The visitors got on the board quick, opening the scoring 1:09 into the game.
After a Flames rush ended with a centring attempt in traffic going through the crease and up to the high boards, the Jets took off on a 3-on-1 and Calgary boy Adam Lowry held the puck and snapped it low to beat Markstrom for his ninth tally of the season.
Just over five minutes later, Calgary's penalty-killers were called upon after Dillon Dube was sent off for cross-checking Jets defenceman Neal Pionk.
They got the job done on the first one and Elias Lindholm recorded the first shot for the homeside not long after, gathering up a loose puck down low in prime-scoring territory and trying to wire one top corner but Hellebuyck flashed the leather to deny him.
The Flames were denied on their lone powerplay of the period.
They got another crack just over five minutes into the second but 20 clicks into it, Lowry scored his second of the night on a short-handed breakaway, sliding the puck five hole with a backhand at 5:33.
Calgary got another powerplay late in the frame but weren't able to beat Hellebuyck and Blake Wheeler would score at 18:46 to give the Jets a three-goal cushion going into the final stanza.
Wheeler added another on the powerplay early in the third.
Markstrom made a penalty-shot save on Andrew Copp with 48.8 seconds left to play after the Jet was hauled down on a breakaway.
Prior to the game, the Flames played a tribute video had a moment of silence to honour former owner Byron (B.J.) Seaman who recently passed away.
