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ST. LOUIS, MO -- Brian Elliott made 23 saves against his former team, and Sam Bennett had a goal and an assist to help the Calgary Flames to a 4-1 win against the St. Louis Blues at Scottrade Center on Tuesday.

Dennis Wideman, Deryk Engelland and Johnny Gaudreau also scored for the Flames, who have back-to-back wins to sweep a two-game road trip after starting the season with one victory in six games.

"I've said right from the beginning, I don't question their will to win," Calgary coach Glen Gulutzan said. "I don't question their want to win. But the manner in which we were going about it wasn't the right way. We're trying to get that straightened out. These are two good steps. This is a great locker room. This is a good group of guys. They care.

"They went for dinner there in Chicago (on Sunday), and it's helping. The tighter we're going to be the better it's going to get for us. We have to learn how to play in this league to win every night."

Elliott spent five seasons with the Blues, going 104-46-16 with a 2.01 goals-against average, a .925 save percentage, and 25 shutouts in 181 regular season games. The win was Elliott's second in as many nights after starting the season 0-3-0.

"I saw that on the schedule from a while ago in the summer," Elliott said. "You want to come back here. I had so much fun playing in front of these fans in this building and wanted to do it again even though it was another team. The guys did a heck of a job in front of me to get that win for me."

Elliott was greeted by fans with chants and a video tribute in the first period.

"It was special for me hearing that and it really got me into the game and get that feeling a little bit," he said. "I'm sure they don't like that result now. It meant a lot, and the video tribute meant a lot. I thought it was coming being the first time back here. I wanted to savor it. There's been times in the past where I was too focused to look. I wanted to take it all in. I had a great time here with my teammates on the other side. It's fun to look back, sometimes."

Kevin Shattenkirk scored, and Carter Hutton made 26 saves for the Blues.

Wideman opened the scoring on the power play 3:54 into the game, taking a pass from former St. Louis forward Troy Brouwer and ripping a shot by Hutton to give the Flames a 1-0 lead. Brouwer's assist was the 300th point in his career. He had 18 goals and 21 assists in 82 games as a member of the Blues in 2015-16.

Engelland doubled Calgary's lead midway through the period. He jumped up into the rush and took a cross-ice pass from Kris Versteeg before pulling the puck to his backhand and lifting it over Hutton to put the Flames up 2-0 at 10:30.

Bennett almost put Calgary up by three on a partial breakaway with 1:51 remaining in the period, but Hutton blockered away his shot.

Hutton couldn't stop Bennett 2:16 into the second period. Bennett worked his way off the boards and into the high slot before shooting through a screen to beat the Blues goaltender to extend the Flames' lead to 3-0. Bennett has goals in back-to-back games, and points in three straight games.

Shattenkirk scored on a 5-on-3 power play at 5:49 of the third period to cut the lead to 3-1, but Gaudreau scored into an empty net with 1:11 remaining in regulation to clinch the win.

"We handled the push that they gave," Gulutzan said. "We got into some penalty trouble there. The 5-on-3 goal was a nice shot. We stayed with our composure and I thought that for two periods we were in control of our game and we put it into a position to have ourselves a win and we came through."

NOTES: The Flames went 1-for-3 on the power play, and killed three of four shorthanded situations. Matthew Tkachuk, who grew up in St. Louis, played after sitting as a healthy scratch in back-to-back games. Mark Giordano played in his 600th career NHL game. Freddie Hamilton, Brett Kulak and Jyrki Jokipakka were scratched for Calgary.

UP NEXT: The Flames will host the Ottawa Senators at Scotiabank Saddledome on Friday (7:00 PM MT; SN-Flames, FAN 960).