Bryan Little and Mark Schieffle also had one goal-one assist nights as the Jets scored twice in the first period, opened up a 4-0 lead after 40 minutes and cruised to their second consecutive win under new head coach Paul Maurice.
Maurice was hired Sunday, the same day that former Jets coach Claude Noel was fired. Winnipeg won 5-1 over Phoenix in Maurice's debut on Monday.
Dustin Byfuglien and Jacob Trouba also scored for Winnipeg (21-23-5). The Jets win for just the second time in their last eight road games.
Mark Giordano and Lance Bouma scored for Calgary (16-26-6), which hits the road for games in Vancouver and San Jose next.
The Flames have been outscored 22-4 during this terrible stretch at the Scotiabank Saddledome, as Calgary broke its previous mark of six straight losses set in December 1998.
Home or away, goal scoring has been a real trouble spot of late.
Calgary has mustered only 12 goals in its last 11 games. They have lost nine of those games to sit 28th in the NHL, three points up on Edmonton. The last place Buffalo Sabres have climbed within six of the Flames.
Winnipeg opened the scoring at 5:01 when Michael Frolik burst down the wing and sent a backhand on net that Reto Berra kicked out into the slot where it was buried by Little for his 16th goal.
The Jets made it 2-0 three minutes later. Byfuglien was left uncovered in the slot and one-timed a set-up from Jokinen.
Calgary's defensive coverage was also poor on both second period goals.
Schieffle was left all alone at the side of the net for an easy tap-in at 9:09, set up neatly by Blake Wheeler. At 17:31 on the power play, nice puck movement resulted in Jokinen having an empty net to fire his 13th of the season into.
Calgary finally got on the scoreboard 40 seconds into the third period when Giordano's shot from the blue-line slipped past Ondrej Pavelec.
Any momentum from that goal was short-lived. Two minutes later, Trouba shook off Matt Stajan and wheeled into the slot where his low wrist shot beat Berra through the pads.
Making his fourth start in a row, Pavelec finished with 20 saves to improve to 13-19-4.
Berra had 18 stops. The 27-year-old first year goaltender from Switzerland falls to 5-14-2.
Notes: Prior to the game, the Jets placed Evander Kane (hand) on injured reserve and recalled Carl Klingberg from St. John's (AHL). Klingberg has played seven career NHL games but has yet to make an appearance with the Jets this year.... Calgary LW Mike Cammalleri (concussion) missed his third game... The Flames next home game is against Phoenix next Wednesday... Two of the coldest Flames are TJ Galiardi with no goals in his last 32 games and Matt Stajan with no goals in his last 16... The next game for both Flames LW Jiri Hudler as well as Byfuglien will be their 500th career NHL game.