Allen, who has started four of five for St. Louis due to the struggles of veterans Brian Elliott and Jaroslav Halak, stopped all 28 shots to win his fourth straight. He is 7-1 since being recalled from the minors last month.
St. Louis have back-to-back wins in regulation for the first time since Jan. 24-25. The Blues have won four of five overall.
Alexander Steen celebrated his return to the lineup for St. Louis with a goal and two assists. Steen, who had missed eight games with a shoulder injury, scored his first goal since Feb. 15.