ST. LOUIS -- Jaroslav Halak needed a wakeup call. He got one in the form of a disallowed goal.
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 score of 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.
The Wild managed just 10 shots over the first two periods, but tested Halak with 12 shots in the final 20 minutes.
"The first two periods, no action for me," Halak said. "I needed to stay focused. It wasn't easy."
Minnesota appeared to take a 1-0 lead when Zach Parise deflected a shot behind Halak just 30 seconds into the game. The on-ice officials ruled he tipped the puck with a high stick. After a lengthy review, the call stood.
Parise was certain that the goal should have counted.
"There is no way my stick was over the crossbar," he said. "I'm 5-10 and I don't think the stick was over my waist.
"That's just the wrong call."
Parise sustained a bruised left foot on a shot by Steen in the first period. Parise played three shifts into the second period before leaving the game.
"We'll find out more (Tuesday)," said Parise, who was walking with a noticeable limp after the game.
Minnesota coach Mike Yeo agreed that the goal should have counted.
"To me, it was clear that it was a goal," he said. "It's fair to say (after that) we came unraveled."
Halak was not sure if Parise's stick was high enough to disallow the goal.
"It was one of those lucky bounces on our side," he said. "If it was a little bit lower, it would have been a goal. Not giving up a goal like that is huge. It would have been a big boost for them."
The Blues needed just 50 seconds to parlay the early break into a 1-0 lead. Sobotka converted off a shot by Carlo Colaiacovo at 1:20. Sobotka also scored the first goal 1:39 into a 6-1 win over Dallas on Saturday.
"We talked about it, that we needed a fast start and we needed to play hard," Sobotka said. "I think we did a good job of that."
Steen broke out of a four-game goal drought by pounding in 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.
"We did a good job of getting pucks through," Steen said. "I thought it was a good game."
Both of the Blues' first-period goals came on rebounds of shots from long range.
"I thought it was of one the best games we've played five-on-five," St. Louis coach Ken Hitchcock said. "We did a lot of good things."
The Wild concluded a four-game road trip at 2-2.
St. Louis has a franchise record 37 points through its first 23 games.
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. He finished with two shots on goal in 5:07. ... 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.