St. Louis has outscored the opposition 5-0 in its last three third periods at home, including three goals against the Rangers to break a 1-all tie.
"We got back to St. Louis Blues hockey in the third," Payne said. "We're just sticking with the plan. We're not there to change our game in the third period. There would be some times when you have to if you're chasing the lead, but when you've got one, it's about keeping your feet moving, it's about moving in sync."
Brian Boyle scored for New York, snapping the Rangers' scoring drought at 172 minutes. The Rangers lost their third straight and fourth in five games (1-2-2).
"I thought we played some good minutes tonight, but again, we just don't score goals," Rangers coach John Tortorella said. "... We've just got to keep on grinding through this and try to find a way to have some sort of consistency.
"The big problem for me right now is our top guys are fighting it. ... I believe they're good people and they'll work themselves out of it."
Polak took a feed from Steen and fired a shot from the right point that deflected in off Rangers defenseman Daniel Girardi's skate 45 seconds into the third period that turned into the winner. It was Polak's third of the season and gave the Blues a 2-1 lead.
"I wasn't too happy about the shot, but somebody deflected it," Polak said. "I think it was their defenseman, but that is why I was mad because I thought I missed the shot and it was in the net."
Steen raced around the right side and around the net before backhanding a shot off Johnson after taking Polak's pass 8:31 into the third period.
"To be honest, I was going a little higher than what happened," Steen said of the shot. "I got kind of lucky, but it bounced off [Johnson's] back and went in. As I came around, I knew he was late coming over."
Johnson, making his third start, said the shot by Steen caught him off-guard.
"I anticipated him going wide, but him being a left-handed shot coming around the net, they usually don't throw a shot on net," Johnson said. "He read me perfectly and I wasn't against the post. He made a good shot, but it's unacceptable. I can't let in goals like that. I misplayed it and he took advantage."
Perron's power-play goal, a one-timer from the left circle off a feed from Tkachuk gave the Blues a 1-0 lead at 14:07 of the first. It was Perron's 13th of the season.
Steen's shot from the point earlier in the first clanged off the cross bar on the Blues' first power play, preventing the home team from leading by two.
Boyle got his fourth of the season after he stripped Blues defenseman Eric Brewer of the puck behind the Blues' goal, skated in front and put a backhander past Mason at 7:37 of the second to tie it at 1.
The Rangers finished with 22 shots on goal and just missed tying the game in the third, but Mason made a point-blank stop on Marian Gaborik.
"The last month, we talked about getting extra saves," said Mason, 4-1-1 in his last six starts. "I wasn't doing it the last month. Games are so close, and every game we seem to play is a tight game. Those saves make a difference and it was nice to be able to make them and keep the guys in."
Backes added an empty-netter with 12.1 seconds remaining.
The Rangers are one of two franchises the Blues have never shut out in their history, now spanning 127 games. Ottawa is the other. ... New York's last regulation loss on the road came on Nov. 28 when it lost to Pittsburgh 8-3. ... Enver Lisin and Aaron Voros were inserted into the lineup for the Rangers, replacing Donald Brashear (hamstring) and Ales Kotalik (healthy scratch). ... Blues RW T.J. Oshie skated in his 100th game. ... Rangers RW Marian Gaborik has 30 points in 29 games against St. Louis. ... Steen has 10 points in 10 games, including seven goals. ... Cardinals ace Chris Carpenter was in attendance.