Paul Stastny continued his mastery of the Flames with three assists, giving him 49 points in 41 games against Calgary. Kevin Shattenkirk had three assists, and Brian Elliott stopped 23 shots for St. Louis.
Vladimir Tarasenko and Alex Pietrangelo scored for the Blues, who are 7-1-1 in their past nine games against the Flames and have defeated Calgary five straight times on home ice, outscoring the Flames 18-6.
In the Blues' 3-2 season-opening loss to the New York Rangers on Thursday, they lamented their start to the game. They trailed 1-0 and allowed 16 shots in the first period. On Saturday, despite a marginal 9-8 shots advantage, the Blues played the style they needed to.
"We had a lot more participants," coach Ken Hitchcock said. "... We managed the puck well, we really did a lot of things. We played on our toes. I thought we did a whale of a job. Still in saying that, we needed Brian today. Brian was really good today."
The Blues scored twice on the power play, they played in straight lines and they got pucks behind the Flames and forced Calgary to play in its zone must of the game.
"We weren't really waiting for the game to come to us and taking it to them," Elliott said. "I think we executed for the most part the whole game. It's fun watching those guys working hard for you in front of you."
Stastny said, "I think we just got more comfortable out there. The first game, we were kind of getting the jitters out of the way. We knew the ice wasn't going to be the best this early in the season. I think we just kept it a little more simple and kind of created chances through turnovers."
"I think the game was in the image of their first goal," Flames coach Bob Hartley said. "A couple of our guys get tangled up and they get a 3-on-1 out of it. Playing a team with so much talent, so much depth, you don't want to give them early momentum and they got [it]."
Lindstrom scored 48 seconds into the game, his first goal since Oct. 13, 2011 when he played for the Colorado Avalanche. He finished a tic-tac-toe play in front after getting a clever pass from Stastny in tight. Lindstrom redirected the puck past Hiller into the open side.
"It was a very nice play by my linemates there," Lindstrom said. "I was holding my stick down and it was an empty net. It was nice."
With Calgary's Matt Stajan off for tripping, Backes redirected Shattenkirk's shot from the blue line past a screened Hiller 8:44 into the first for a 2-0 lead. The Blues were aggressive, assertive and played the puck in Calgary's zone for much of the first 10 minutes.
"We played simple early," Shattenkirk said. "We played hard and we did the things that make us successful. We chipped pucks in, played a physical game, and were able to be successful on the power play and 5-on-5 as well."
Pietrangelo's first goal gave the Blues two power-play goals in two tries; he collected a shot from Shattenkirk off the end boards around to the right circle. Pietrangelo wasted little time blasting a one-timer past Hiller 3:12 into the second period to make it 3-0.
Tarasenko made it 4-0 at 7:10 of the second when he one-timed a shot from the low slot after Jaden Schwartz dug a puck out from behind the net and flipped it in front.
Hiller, who allowed four goals on the first 15 shots, kept the game 4-0 with several strong saves as the second period progressed. He faced 19 shots in the period.
"They outworked us," Hiller said. "I don't think that we have the kind of team where we can just count on talent. We have to work hard, and when we get outworked, it's not going to go well."
Glencross broke up Elliott's shutout when he deflected Mark Giordano's wrist shot from the blue line at 15:47 of the third. The assist was Giordano's 200th NHL point.
"The third period, I thought we skated better, but [the Blues] were by far the better team," Hartley said.