He scored 40 seconds apart in the third period to give Chicago the lead and the Blackhawks poured it on to beat the Nashville Predators 6-3 Sunday night.
"In the third period, we started moving our feet and did the things we needed to win," Brouwer said.
Dave Bolland also scored two goals for the Blackhawks, who lost 3-2 in a shootout the night before in Nashville.
"We know when we work hard, things fall into place for us," Toews added. "We wanted to give it back to them tonight. We went down a goal, but just kept working through it."
J.P. Dumont had two goals for the Predators, who are 7-2 in their last nine. Martin Erat added a power-play goal for Nashville.
Nashville defenseman Shea Weber extended his scoring streak to a career-high nine games with an assist. He has three goals and 10 assists during the span.
Brouwer's first goal tied it at 3 on a power play. He cleaned up Duncan Keith's drive from the top of the slot at 9:19 of the third.
Shortly afterward, he powered out of the right corner, cut into the slot and fired in a high shot with Toews screening Nashville goalie Anders Lindback at 9:59.
"We stopped playing our game and they came at us pretty hard," Dumont said. "We took a penalty and they got the momentum back. It's just the kind of game that we let them take it away in the third."
Lindback stopped 28 shots in place of Pekka Rinne, who started 10 of Nashville's previous 11.
Erat opened the scoring with a power-play goal at 2:04 of the first to end a streak of eight scoreless advantages. He fired in a rebound from the left side of the crease.
Bolland tied it at 1 just over four minutes later after Bickell forced Nashville's Kevin Klein to turn over the puck along the boards in the Predators' zone. Bickell plowed to the net with the puck and his shot was stopped by Lindback, but Bolland punched in the rebound.
Dumont's first goal, on a power play with 5:45 left in the first, came when Chicago defenseman Brian Campbell blocked Weber's drive from the left point, and the puck bounced to Dumont.
Bolland scored again with 8:02 left in the second to tie it at 2. He beat Ryan Suter one-on-one in the slot with a flashy stickhandling move, then fired a low shot past Lindback.
"When I went around Suter, I was sort of dumbfounded," Bolland said.
Dumont gave the Predators a 3-2 lead at 3:45 of the third when he scored from a faceoff in the Chicago zone.
"We didn't play really well last night, but we found a way to win and came back in the third and gutted one out," Weber added. "Tonight we just found a way to get the lead and then found a way to blow it."
Bickell made it 5-3 from the slot with 5:52 remaining and Toews completed the scoring with 3:35 left.
- Predators D Francis Bouillon sustained a lower-body injury in the first period and didn't return.
- Nashville RW Marek Svatos missed his second game with a lower-body injury.
- The Predators recalled RW Matt Halischuk from Milwaukee of the AHL on Sunday and assigned RW Andreas Thuresson to Milwaukee.
- Nashville D Shane O'Brien served the second game of a two-game suspension for high-sticking Florida's Stephen Weiss last Thursday.