''We talked a little bit before the game that the last few games we've been a little bit stagnant,'' Brouwer said, ''so we wanted to be a difference-maker tonight and we were.''
Stastny's four-point game, his first since signing with the Blues before last season, fueled the line's eight-point effort.
''I think we just work for each other,'' Stastny said. ''We're getting more and more comfortable. I think we've had chances and today they started falling.''
Vladimir Tarasenko and Kevin Shattenkirk also scored for the Blues, who have won four of five following a five-game losing streak. Brian Elliott followed up his career-high 46 saves Saturday by stopping 36 shots against Pittsburgh.
''He's competing at a very, very high level now,'' St. Louis coach Ken Hitchcock said. ''He's taking advantage of a situation that was thrust upon him, but his competitive level's as high as I've seen it right now. It's really good to see.''
Evgeni Malkin and Chris Kunitz scored, and Kris Letang had two assists for the Penguins. They have lost three of four and five of seven. Jeff Zatkoff, making his first start since Dec. 31, stopped 20 shots.
''We didn't execute like we wanted to,'' Penguins center Sidney Crosby said about his team's play in the third period. ''Especially after we did in the first and second. We need to give a bigger push than that with a tied game in the third. They were better in the third, I thought. The first two periods we gave ourselves a good chance, but the third period was kind of the story of the game.''
Steen scored first, with 8 minutes left in the opening period, after Zatkoff left the crease to challenge Brouwer for a puck. Stastny then fed a pass in front and Steen, who hit the post earlier, buried it for his 14th of the season.
The Penguins tied it with Kunitz's eighth of the season, on a breakaway after a spring pass from Letang with 1:57 remaining in the first. Crosby picked up the secondary assist, giving him six points (two goals, four assists) in four games.
Malkin and Tarasenko traded highlight-worthy goals late in the second.
Malkin netted his 20th of the season with 4:04 left in the period after taking a pass from Carl Hagelin, skating past Jay Bouwmeester and beating Elliott with a wrist shot. Letang earned another assist.
With that goal, Malkin reached 20 for the third consecutive year and eighth time in 10 seasons.
Tarasenko answered with his 25th, assisted by rookies Joel Edmundson and Robby Fabbri, with 2:46 remaining in the period after skating around Ben Lovejoy and slipping a shot past Zatkoff to tie the score.
''The battle of the Russians there,'' Stastny said. ''I think once Malkin had that nice goal, then Vladi got upset. He took it in his own end and basically did the same thing a little nicer, a little more power move and a nice shot. I think that was a big response.''
The Blues took control with three goals in the third.
''We knew St. Louis was going to push back in the third period,'' Pittsburgh coach Mike Sullivan said. ''We dominated the second period and they're a proud team, a good team. We knew they were going to push back. We've just got to find a way to match the urgency through that stretch and control that momentum and we didn't do that.''
Brouwer scored the go-ahead goal 2:10 into the period on a one-timer from the slot after taking a pass from Stastny.
Stastny scored, with an assist from Brouwer, with 8:22 remaining. Shattenkirk added an empty-net goal, assisted by Steen and Stastny, with 15.1 seconds left.
The Blues improved to 18-2-4 when scoring three or more goals. The Penguins fell to 2-7-1 in the second game of a back-to-back set.
NOTES: Bouwmeester returned after missing four games with concussion-like symptoms. ... St. Louis recalled D Andre Benoit from the American Hockey League on Sunday. He replaces D Robert Bortuzzo, out with a lower-body injury sustained in Saturday's game. ... The Penguins recalled D Derrick Pouliot from Wilkes-Barre/Scranton of the AHL. ... The attendance of 19,312 was the Blues' 12th sellout.