David Perron scored the winning goal in the shootout and the Blues, despite being outshot 41-18, beat the Jets 3-2 on Saturday.
Perron moved in on goalie Chris Mason in the fourth round of the shootout and roofed a backhander to give St. Louis a surprising victory.
Jaroslav Halak made 39 saves for the Blues, who improved to 2-0 on their six-game road trip. The Blues also beat Nashville in a shootout in the opener of their trip.
Hitchcock was impressed that his team found a way to win while playing their third game in four days.
"This is a very difficult travel situation, so I'm very happy with it," he said. "[The Jets] are sitting here waiting for us, and we still come in and collect points. It's two points ... any points you get on the road are really gratifying. You put them in the bank and move forward.
"Our goalie was our best player and he needed to be."
Blake Wheeler scored both goals for the Jets and had the only tally in the shootout for Winnipeg.
St. Louis forward T.J. Oshie, who had a pair of first-period assists, said Halak was the only reason the Blues were still in it.
"We stole one," Oshie said. "They definitely took it to us. And if it wasn't for Jaro, it could have been 6-2. We took advantage of a very hot goalie and we were able to steal one."
The Blues led 2-0 after the opening period despite getting outshot 16-6.
David Backes opened the scoring at 7:43 with his 18th goal, converting a perfect pass from Oshie with a shot past Mason. Oshie set up the second goal with 46 seconds left in the period, sending a cross-ice pass to a streaking Perron, who beat Mason for his 12th of the season.
The Jets cut the lead in half when Wheeler scored his 12th at 4:49 of the second, firing a rebound past Halak.
Wheeler later knocked one in on a goal-mouth scramble to make it 2-2 with just over 4 minutes left in the middle period.
The third period was scoreless and neither club had a shot on goal in overtime.
Mason made 14 saves for the Jets.
"We got a point against one of the top Western teams, so the guys did a great job," said Mason. "It's just too bad we couldn't get the extra [point]."
He said letting a point slip away in the shootout shouldn't demoralize his team.
"We feel we outplayed them and the shot total was pretty indicative of what happened," he said. "We were strong on the puck, physical, threw pucks at the net ... we're going to focus on the positives."
Dustin Byfuglien had two assists for Winnipeg.
- Jets F Antti Miettinen, placed on waivers by the club Friday, was in the lineup Saturday on a line with Nik Antropov and Tim Stapleton. Miettinen agreed to waive his no-movement clause after being approached by management.
- Winnipeg-born F Alexander Steen, the son of former Jets great Thomas Steen, did not play for the Blues. He's been out since just after Christmas with a concussion. But he was in the press box Saturday, spotted having a chat with former goalie and TV analyst Darren Pang. Steen's dad is now a Winnipeg city councillor.