St. Louis has won seven of nine and is off to the fastest start in franchise history with 12 wins in its first 17 games.
Colorado lost back-to-back contests for the first time this season.
T.J. Oshie added four assists for the first four-point game of his career.
The Blues were 3 for 4 on the power play, breaking out of a 1-for-15 skid that spanned the previous five-plus games. Roy, Backes and Stewart scored on the power play. Oshie had two power play assists.
"We simplified and started shooting the puck," Backes said. "We got a few ugly ones in front to start it off. From that, we hopefully learned our lesson that scoring one out of 20 that are pretty isn't worth it, when we can score a couple a game if we just do things the hard way and shoot the puck."
The three man-advantage goals are a season-high for the Blues.
"A lot of it has to do with how much we were shooting the puck," Oshie said. "We were getting to the right spots and getting some bounces. The last couple of games, I don't think we were getting those bounces.
"Tonight we were shooting and we found the net."
Steen, who pushed the lead to 3-1 with his first goal at 7:16 of the second period, has a point in 12 successive games, a career high. He took a slash in the third period and was not available after the game, though St. Louis coach Ken Hitchcock said Steen was fine.
St. Louis goalie Jaroslav Halak improved to 10-2-2.
The Blues had just one power play goal in their previous five games.
"We've had a lot of good looks on the power play, but tonight, we were rewarded for our looks," Hitchcock said. "I thought the Backes unit showed great continuity. It looked like they were threat every time."
Avalanche goalie Jean-Sebastien Giguere lost for the first time this season after winning his first five starts. He was pulled in the second period after allowing three goals on 14 shots, but re-entered at the start of the third. Giguere, who gave up five goals on 165 shots in his first five games, was looking to become the first Colorado goalie to begin the season 6-0. He finished giving up five goals on 23 shots.
The Blues scored four times over 11:50 in the second period to break open a 1-1 game.
"It feels good to be playing the right way and get a win against a good team," Oshie said.
Backes put his team ahead to stay 2-1 with a power play goal 2:49 in the second period. He jumped on a rebound at the side of the net off a shot from Roy.
Roy, who added two assists, got the St. Louis attack started with a power play goal just 1:54 into the game. It was the first man-advantage goal given up by Colorado on the road this season. The Avalanche were 20 for 20 on kills over their first seven road games.
Colorado appeared frustrated after the four-goal blitz, taking three fighting majors in the final 3:14 of the second period. Three Colorado players were given 10-minute misconducts in the third period.
"They scored on three power plays and that was the story," Colorado coach Patrick Roy said. "I think it's a good learning process for us."
The Blues have scored first in their last nine games.
NOTES: The Blues signed D Carlo Colaiacovo to a one year free-agent contract. He was not in uniform on Thursday. ... The Avalanche had given up two goals or less in nine of their previous 10 games. ... The Blues had 10 shots or more in their last eight periods. ... The game featured three fights in the second period after the Blues took control.