Vancouver's Mason Raymond forced overtime when he beat Allen with just 1:47 left in the third period to make 3-3, but the first-year netminder refused to remain despondent.
Allen made five saves in overtime, finishing with 28 overall, and blocked Vancouver's two shootout attempts to ensure St Louis (9-5-1) won for the third time in a row and he remained unbeaten in his first three starts.
"I am not getting too far ahead of myself," Allen told reporters, having been filling in for starter Jaroslav Halak, who has been sidelined with a groin injury since Feb. 1 but is finally ready to play.
"You are not going to win forever you just want to keep making the most of your chances."
Ryan Kesler scored the first goal of the game, in only his second contest of the season after recovering from injury, and Henrik Sedin added another to give Vancouver a 2-1 first period lead after T.J. Oshie had equalised for the visitors.
Andy McDonald netted an equaliser in the second and Patrik Berglund's deflection in the third put St Louis 3-2 ahead before Raymond completed the scoring.
Oshie and McDonald each netted shots in the shootout to give the vising Blues a perfect three-game road trip.
"We kind of got shocked into playing the right way after a home stand that was definitely less than stellar," said captain David Backes. "We knew it was time to put up or shut up."
The Canucks (8-3-3) have now lost two straight since ending a six-game winning streak but still lead the Northwest Division by three points over Minnesota.
Roberto Luongo had 20 saves in the loss to end his streak of four straight victories. He has, however, yet to lose a start in regulation this season.
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