The game was halted in the second period when defenseman Jacob Trouba was stretchered off the ice following a crash into the boards.
Tobias Enstrom scored the tying goal in the third and Evander Kane also scored for the Jets. Ondrej Pavelec made 29 saves.
Alexander Steen scored a pair against his hometown team as giveaways helped the Blues to an early lead.
David Backes also scored for the Blues, who were coming off a 3-2 shootout win over Chicago on Thursday night.
Trouba missed a hit early in the second period and slammed his head into the boards, bending his neck back at an ugly angle. The Jets' top 2012 draft pick didn't move on his own after he crumpled to the ice.
Both benches emptied as worried players gathered around.
Trouba managed to wave as fans shouted his name while he was being wheeled off. A Jets spokesman said Trouba was taken to the hospital for X-rays and was alert, communicating and moving all his limbs.
The Jets put pressure on the Blues early and were ahead on shots, but it was Backes who scored first from the slot at 8:43. T.J. Oshie fed him the puck on a defensive slip by Grant Clitsome.
It energized the Blues, but then Jokinen evened things up at 15:30 when he fired a bouncing rebound past St. Louis backup Brian Elliott, who finished with 26 saves in his first start this season.
The play also gave right wing Matt Halischuk his first point as a Jet for the assist.
Less than three minutes later, Trouba whiffed on a pass and presented the puck to the Winnipeg-born Steen, who skated into the slot to put the Blues ahead 2-1.
It could have been worse. The Blues also made Winnipeg's goal posts ring like church bells in the first period.
Play stopped for several minutes early in the second and the arena was silent after Trouba's accident.
Neither team scored on the power play in the first two periods although the Jets only had one chance.
St. Louis had three, two thanks to Kane, who spent some time warming the Winnipeg bench after the second.
The Jets lost another defenseman early in the third period when Mark Stuart limped to the dressing room after sliding into his own net.
Steen was perfectly positioned beside the Winnipeg net at 3:34 of the third to one-time a rebound off Backes's glancing shot from the boards and make it 3-1.
But Kane brought the Jets within one at 13:13 when his slap shot from outside the faceoff circle glanced off St. Louis defenseman Roman Polak's stick.
Then Enstrom slammed home a pass from Dustin Byfuglien at 18:06 to tie it up.
Bryan Little and Andrew Ladd connected for the Jets in the shootout and Oshie and Steen hit for the Blues, until Jokinen beat Elliott on his glove side to win the game in the seventh round.
NOTES: Former Winnipeg Jet Thomas Steen (1981-95), father to Alexander and a Winnipeg city councilman, was on hand for the Blues' second visit to the city since the Jets were reborn in 2011.