Sobotka scored from close range at 2:16 of overtime to give the Blues a 5-4 victory over the Minnesota Wild on Sunday night.
St. Louis is 5-1, its best start since winning seven of its first eight in 1997-98. Coming off a 4-3 victory in Dallas on Saturday night, the Blues also improved to 3-0 at home.
Andy McDonald circled around the net and fed Sobotka for the winner.
"I just saw it landed right on my stick and it was kind of a weird shot, but it landed up in the net and I was happy," he said.
Minnesota's Dany Heatley forced the overtime, tying it at 4 when he batted the puck out of the air with 4:08 left in regulation for his fourth goal of the season. The Wild have lost three straight.
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.
"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.