Eriksson put Dallas up for good 4 1/2 minutes later with Alex Steen off on an elbowing penalty.
Kari Lehtonen made the lead hold up, turning aside 35-of-36 for the Stars, who took both ends of a home-and-home series with the Blues.
St. Louis suffered its first regulation time home loss since last March, going 14-0-1 during the span.
B.J. Crombeen got the Blues' only goal and Jaroslav Halak made 21-of-23 saves while absorbing the loss.
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