Steen stickhandled his way through two defenders 6 minutes into the third period and put a shot past Roberto Luongo for an unassisted tally, breaking a 2-2 tie.
He also scored in the first period and assisted on Matt D'Agostini's second-period goal, helping the Blues snap a five-game winless skid.
Jaroslav Halak stopped 21-of-23 shots in the victory.
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