Justin Faulk and Sammy Blais each had a goal and two assists, and Zach Sanford and Ivan Barbashev also scored for the Blues, who posted a season high for goals in a game.
''The guys are confident in what our game looks like when we're doing the right things, we're doing the little things and we're playing for each other and when we do that, we can beat anyone on any given night,'' Schwartz said.
Jordan Binnington made 23 saves as St. Louis won its second straight.
Zach Parise scored and Kaapo Kahkonen made 29 saves for the Wild, who allowed a season high in goals for a game. Minnesota has given up 17 goals in its last three games.
''They started great, we started bad,'' Wild coach Dean Evason said. ''Everything that's been poorly done all year was poorly done, not only early, but often and throughout the game.''
The Blues took control with a season-high four goals in the opening period.
Sanford gave the Blues the lead just 92 seconds into the game. It was just the 14th time this season that St. Louis scored first and it improved to 8-1-5 when taking an early lead.
''Our mindset was being aggressive, and closing plays out, and when we had the puck, we moved it fairly quick,'' Blues coach Craig Berube said. ''We talked about getting pucks in behind them and right from the get-go and I thought we did that.''
Schwartz made it 2-0 Blues at 5:59 of the first, ending a 17-game scoring drought.
Parise got the Wild on the board 34 seconds later off a rebound from a shot by Carson Soucy. It was his first goal in 14 games.
''I think that their puck support was really good tonight,'' Parise said. ''They were able to hit the middle a lot. They were able to make short little passes to get out of the zone and even in the offensive zone for them. It seemed like they always had two guys around the puck, and we were getting outnumbered.''
Schwartz scored his second of the game with 4:37 left in the first as Brayden Schenn found him unmarked in the slot.
''He's a type of player that really, (brings) energy and really drives our bus almost,'' Berube said of Schwartz. ''He skates and works on pucks and hounding and checking.''
Blais made it 4-1 about 90 seconds later with a one-timer off Faulk's feed from behind the net.
O'Reilly effectively put it away with two early goals in the second period, including an unassisted short-handed score a few minutes later that made it 6-1.
O'Reilly completed his second career hat trick in the third with a deflection of a shot by Jake Walman. Walman was originally credited with the goal, but it was changed to O'Reilly after the game.
The nine goals scored by St. Louis was one more than it totaled during a seven-game winless streak from March 22-April 5.
''It's nice to help our goaltenders too and score some goals,'' O'Reilly said. ''Putting the puck in the net is a good feeling. So, it's something we want to continue, that's for sure.''
The Wild had their streak of four straight games with a power-play goal snapped after going 0 for 2 with the man advantage. Minnesota entered the game second in the NHL with the man advantage since March 10, going 27 percent (13 for 48) in that span.
TAKING A SEAT
Blues F Mike Hoffman and D Robert Bortuzzo were healthy scratches for the second consecutive game. Hoffman, who signed a one-year, $4 million contract at the start of the season, has been scratched in three of the team's last six games fueling speculation that he could be moved before the trade deadline.
The teams play again twice in the next three days - back at Enterprise Center on Saturday night and at Minnesota on Monday night.
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