''We had to win one game to get things going back in the right direction,'' said Blues defenseman Alex Pietrangelo, who had two assists. ''There's nothing better than playing against an opponent like this, division rival, big game for us.
''We know what they've done, and coming in after losing to them in the playoffs last year certainly gives it a little bit of an extra edge. I thought we all stepped up to the plate.''
The Blues (3-3-1), who lost in six games to the Blackhawks in the first round of the playoffs last spring, had scored just once in losing back-to-back games to Anaheim and Vancouver. They had dropped three of four games, including a shootout defeat in Los Angeles.
''We hit a bit of a lull the last two games and we needed a great performance, and who better than our biggest rivals to bring it out of us,'' Blues captain David Backes said. ''Guys put together a heck of a 60-minute effort.''
Brian Elliott made 22 saves for St. Louis, including nine in the third period. Antti Raanta made 28 saves for the Blackhawks.
The Blackhawks (4-2-1) have dropped two straight in regulation, falling again after being beaten in Nashville on Thursday.
The Blues committed two penalties within the first minute, and the Blackhawks took advantage with Patrick Sharp's 5-on-3 power-play goal, assisted by Patrick Kane and Marian Hossa, just 1:02 into the game.
''The first five minutes were a little bit of a whirlwind, and everybody kind of calmed things down, and we got our game going,'' Elliott said. ''That's the way we need to play, just that even-keeled mentality. In a high-intensity game against a good opponent like that we responded from our last couple games, not really burying and not really putting away teams when we had the chance.''
The Blues tied it when Schwartz scored his team-high fifth goal of the season. Schwartz beat Raanta between the pads with 7:45 left in the first period.
St. Louis scored twice in the final two minutes of the second period.
Reaves netted his first of the season with 1:51 left in the period following a video review that showed he knocked in a rebound of Maxim Lapierre's shot.
''I don't know how the rules are but I made a save, and the guy came and pushed me into the net, and then the puck came over the line,'' Raanta said. ''I think that was a little bit like goalie interference or something.
''You can't say anything, but of course that was a little bit like a bad call by the refs, but it's hard to say what they were seeing. It felt a little bit like a bad goal, but I don't know what else I should say.''
Jaskin, recalled from Chicago of the AHL on Friday, then put in a rebound of a shot by Pietrangelo with 6 seconds remaining for his second career goal.
''That was huge for us,'' Jaskin said. ''Even that second goal just got us going, and that was really important. We really started playing better.''
Kris Versteeg took a nice crossing pass from Sharp and beat Elliott with a high wrister over the goalie's stick-side shoulder to make it 3-2 at 2:37 of the third period.
''We scored a goal and had some momentum back but didn't get the equalizer,'' Blackhawks coach Joel Quenneville said.
NOTES: The Blues have won four straight regular-season home games against the Blackhawks, the first such streak in the series since March 3, 1998-Jan. 7, 1999. ... Chicago G Corey Crawford missed his third consecutive game due to an upper-body injury. ... St. Louis forward Paul Stastny, placed on the injured list on Friday, missed his third straight game. ... Quenneville and St. Louis coach Ken Hitchcock are the active leaders in victories. Quenneville has 710, and Hitchcock has 660. ... Both of Jaskin's goals have come against the Blackhawks. ... Quenneville said LW Daniel Carcillo could be out multiple weeks after hurting his right knee on a hit from T.J. Oshie early in the third period. ... The attendance of 19,434 was the second sellout for the Blues in four home games this season.