"We feel like we're an elite team," Getzlaf said. "And now we're starting to show it."
Anaheim won its second in a row, after beating defending Stanley Cup champion Chicago 3-2 in a shootout Friday. The Ducks' 45 points are tied for the most in the league with Chicago.
St. Louis lost for the third time in four games and fell to 12-2-2 at home.
Anaheim completed a four-game run against the Western Conference elite with six points. The Ducks lost in overtime to San Jose and Los Angeles.
"This stretch has been big for us," Getzlaf said. "We're playing with a lot of confidence and we believe we can fit in with the best teams in the league."
Anaheim coach Bruce Boudreau agreed.
"What we've proved at this stage of the year is that we can play with the big boys and compete with them," he said. "We're going to leave (here) feeling good about ourselves."
Chicago, St. Louis, San Jose and Los Angeles are a combined 76-24-17.
Getzlaf, who added an assist, has a point in his last 13 games. He has 10 goals and 10 assists during that span.
Getzlaf missed three games in November with an injury and has a point in his team's past 11 games, the longest current run in the NHL.
Andersen, who won his first six starts, improved to 8-1 with his second successive victory. He leads all rookie goalies in wins.
Anaheim scored three times in the opening 7:29 to chase Blues goalie Jaroslav Halak, who faced eight shots.
Cogliano got it started by banking in a shot off the skate of Barret Jackman after just 70 seconds. Perry scored his team-high 18th on the power play at 5:36. Getzlaf capped the early blitz with a drive from the faceoff circle.
"We knew they would make a big push and we had to meet it head on," Getzlaf said. "We did a good job of doing that."
Andersen said the three early goals made his job a lot easier.
"But you still have to force yourself to stay sharp," he said. "If we can score three goals that quick, they can, too. They fired a lot of shots, but most of the time I was able to see the puck through traffic."
Halak was pulled for the third time this season.
"I need to look at myself and everybody else needs to probably find the answers," Halak said. "We need to play for 60 minutes, not only for 20."
Bonino converted at 17:16 of the second period to push the lead to 4-0.
Andersen stopped the first 20 shots he faced and helped kill off 4-minute power plays in each of the first two periods.
The Blues have struggled in the first period of late, falling behind San Jose 4-0 and Los Angeles 2-0 in the past four games.
"We're obviously not getting ready to play," Berglund said. "It's hard to get back against a good team like Anaheim."
NOTES: Anaheim RW Teemu Selanne was a healthy scratch after playing Friday in Chicago. The 43-year-old has played on back-to-back nights only once this season. ... St. Louis C Derek Roy is one assist shy of 300 for his career. ... The Blues are an NHL-best 57-16-8 at home since the beginning of the 2011-2012 season. ... Anaheim G Jonas Hiller was given the night off after facing 76 shots and 12 shootout attempts in the previous two games. ... St. Louis has scored at least two goals in all 16 home games this season.