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."
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.
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ST. LOUIS, MO - DECEMBER 07: St. Louis Blues fans hold up signs before a game against the Anaheim Ducks on...