Blues coach Ken Hitchcock wasn't certain how his team would respond after playing six games in nine days.
"I've been around a long time, but the third period was impressive," Hitchcock said. "Back to back, it was a very physical game last night, and to come with that type of effort was a real confidence booster. We didn't get down on ourselves. We really took our game to another level."
After taking a 1-0 lead in the first, the Blues gave up three consecutive goals before rallying.
"We kept battling. We kept battling and (Sobotka) capped with a great overtime goal," Jackman said.
Zach Parise had two goals and an assist for Minnesota after also scoring twice in the Wild's 5-3 loss in Detroit on Friday night. Mikko Koivu added a goal, and Niklas Backstrom stopped 32 shots.
"It doesn't matter, we lost the game," Parise said. "We have to win games here."
Stewart and Jackman scored 2:18 apart midway through the third to give the Blues a 4-3 lead. Stewart tied it with his fourth goal, a deflection off Alex Pietrangelo's shot, and Jackman put the Blues in front.
Parise scored on Minnesota's first two shots in the second period, both on power plays, to give the Wild a 2-1 lead. Koivu added a goal on a 4 on 4 to make it 3-1 in the second, but Berglund countered 1:01 later to pull the Blues within one.
Redden scored for the second consecutive night for the Blues after going nearly three years without an NHL goal. He slapped a shot from near the left boards about midway through the first period to open the scoring.
St. Louis entered the game as the best power-play team in the NHL, converting seven of 16 opportunities, but failed on five chances against the Wild, with just three shots.
Minnesota took three penalties in the first nine minutes of the third period. Despite not giving up a goal while a man short, the extra work tired the Wild.
"It was a recipe on how to lose a game," Wild coach Mike Yeo said. "The bottom line is we can sit here and talk about our potential, the fact that we have a nice team on paper. (But) the winners do things that it takes to win hockey games."
The Blues wore jerseys with No. 6 and "Musial" on the back during pregame warmups in honor of St. Louis Cardinals great Stan Musial. He died Jan. 19. Musial's funeral and burial were held Saturday. The jerseys will be auctioned with proceeds going to charitable arms of the Cardinals and Blues. ... After playing its first six games in nine days, St. Louis gets three days off before playing Thursday night at Columbus.
Copyright by STATS LLC and The Associated Press
Arena: Scottrade Center Location: Saint Louis, Missouri
Referees: Ian Walsh, Ian Walsh Linesmen: Brian Murphy, Derek Nansen
Attendance: 18,265 (95.4% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Wade Redden (2)
Assists: David Backes, David Perron
Zach Parise (4)
(Power Play) Assists: Tom Gilbert, Ryan Suter
Zach Parise (5)
(Power Play) Assists: Mikko Koivu, Dany Heatley
Mikko Koivu (1)
Assists: Zach Parise, Tom Gilbert
Patrik Berglund (3)
Assists: David Perron, Alex Pietrangelo
Chris Stewart (4)
Assists: Alex Pietrangelo, Kevin Shattenkirk
Barret Jackman (1)
Assists: Vladimir Tarasenko, Kevin Shattenkirk
Dany Heatley (4)
Assists: Matt Cullen, Ryan Suter
Vladimir Sobotka (1)
Assists: Andy McDonald, Roman Polak