Kari Lehtonen made 24 saves for the Stars (16-12-1), who have lost two in a row after a five-game winning streak. They were shorthanded seven times and allowed two power-play goals.
"I think it's more why we took the penalties," Dallas coach Ken Hitchcock said. "We took the penalties because we were second place to the puck. They won the race and we took the penalty because of it. We got beat, got beat to a lot of the races on the penalties we took, poor stick positioning, poor sticks. Any momentum we started to build, we got it taken away with penalties."
Schenn's 14th goal of the season gave the Blues a 1-0 lead at 13:39 of the first period off a rebound to the right of Lehtonen. Schenn had a hat trick in a 4-3 win against the Montreal Canadiens on Tuesday.
"That's just a great play by [Alexander Steen], where he was able to get a puck through, and I think [it was] me and [Dmitrij Jaskin] 2-on-1 pretty much in front of the net," Schenn said.
The Blues had four power plays in the first period, including a 5-on-3 for 1:14, but did not score.
Stars defenseman Stephen Johns almost tied the game in the final second of the second period. His shot hit Allen and popped over the goalie into the net, but video review confirmed the puck went in after the period ended.
"The horn's always delayed in every arena," Allen said. "It's usually a second delayed, so you always know once the horn (sounds) ... the puck's in the net is probably the same time as the horn, so you always know it's late."
Parayko scored on a one-timer from the blue line at 5:01 of the third period, the Blues' second power-play goal, for a 2-0 lead. Paul Stastny set a screen in front of Lehtonen.
"They kind of went out to [Patrik Berglund] on the wall, and they were already on [Tarasenko] on the other side," Parayko said. "So it kind of seemed like I was alone in the middle. Great net-front by our team."
Tarasenko scored an empty-net goal with 48 seconds remaining, his first goal in seven games, 13th of the season.
