Steen has 19 goals this season, one behind Washington's Alex Ovechkin for the NHL lead.
Vladimir Sobotka also scored for the Blues, who are 9-1-1 in their last 11 and 12-2-1 in the last 15. They have won six straight against Minnesota by a combined 20-7.
The Wild were shut out for the first time this season and lost only their second game in the last eight. Minnesota (15-6-4) is still off to its best start with 34 points in its first 25 games.
Halak improved to 13-3-2 with his third successive win. He robbed Zenon Konopka from close range late in the second period and earned his second shutout of the season and 27th of his NHL career.
Steen pounced on the rebound of Jay Bouwmeester's shot midway through the first period to give the Blues a 2-0 lead. Steen added an empty-net goal with 1:22 left.
Sobotka scored just 1:20 into the game off a rebound of a shot by Carlo Colaiacovo. Sobotka also scored the first goal 1:39 into a 6-1 win over Dallas on Saturday.
Minnesota goalie Niklas Backstrom, who started in place of Josh Harding, fell to 2-2-2. Harding is day-to-day with a groin injury.
St. Louis has a franchise record 37 points through its first 23 games.
NOTES:St. Louis D Kevin Shattenkirk missed the game because of the flu. ... Minnesota LW Mike Rupp made his season debut after missing 24 games due to offseason knee surgery. ... This was the first of five meetings between the new Central Division rivals. ... The Blues lead the NHL with a plus-32 goal differential. ... St. Louis LW Ryan Reaves underwent surgery Monday for a broken bone in his right hand. Reaves, who leads the team with 69 hits, is expected to miss at least six weeks. ... Minnesota has failed to score on its last 11 power plays against the Blues.