Mark Scheifele took a Josh Morrissey feed at the left hash mark along the boards before curling into the top of the circle and feeding Connor with a cross ice pass.
The Jets leading scorer in the regular season made no mistake, snapping the disc past Jordan Binnington, beating him glove side to give the Jets a 4-3 lead to complete the comeback.
Winnipeg trailed St. Louis after two periods before firing three third period goals to take game one.
“You’ve just got to stick with it, stay positive, knowing you’re doing the right things, getting the chances. You know a lot of plays like those cross-ice plays, even the one that Fetsy (Cole Perfetti) made on the power play. I’m trying to get that off as quickly as possible, near a lot of holes in the goaltenders if you can. It was obviously a great play by Scheif. Just try to get it off quick," said Connor.
Scheifele just wanted to get the puck on his stick and let Connor work his magic.
"Oh it’s amazing. All I want to do is put the puck in his hands and he does some fantastic things. Like I said before, I’m lucky to play with him. He’s absolutely fantastic, he shoots the puck fantastic, he does so many little things fantastic. Like I said a million times, he’s amazing to play with," he said.
Connor and Scheifele each had three point nights with a goal and two assists.
Alex Iafallo Jaret Anderson-Dolan and Adam Lowry also scored for Winnipeg.
Josh Morrissey had a pair of assists.
Connor Hellebuyck made 14 saves to pick up the win for the Jets.
Robert Thomas, Oskar Sundqvist and Jordan Kyrou scored for the Blues.
Justin Faulk had a pair of assists for St. Louis.
Jordan Binnington turned aside 21 shots for the Blues.
Robert Thomas opened the scoring on the power play 9:31 into the first.
With Luke Schenn off for interference, Thomas converted a Cam Fowler feed just inside the left face off circle and beat Hellebuyck with a glove side wrister.
The goal was his first of the playoffs.
Mark Scheifele tied the game at 13:38 with a power play goal.
With Jake Neighbors off for slashing, Kyle Connor got Scheifele the puck just outside the Blues crease.
Scheifele's shot went in off of Blues defenceman Ryan Suter's outstretched stick past Binnington to make it 1-1.
The Jets took the lead at 15:02 when both Morgan Barron and Jaret Anderson-Dolan tipped a Luke Schenn shot from the point past Binnington to make it 2-1.
Oskar Sundqvist tied it up 18:10 into the first when Luke Schenn blocked a shot with his skate and the puck ended up right on Sundqvist's stick.
He beat Hellebuyck with a high shot to make it 2-2.
Jordan Kyrou scored 1:13 into the second when he drifted a high wrister past a screened Hellebuyck to give St. Louis a 3-2 lead.
Alex Iafallo tied the game 9:18 into the third when he slid a puck from close in past Binnington to make it 3-3.
Adam Lowry added an empty netter to seal the win for the Jets.
Blues Head Coach Jim Montgomery was succinct in his assessment of his club's play in game one.
"I didn't think our puck management and decision making was quick enough," said Montgomery. "Our habits weren't very good tonight. We weren't very good tonight. We'll grow, we'll get better."
SHOTS-ST LOUIS 17 WINNIPEG 26
ATTENDANCE-15,225