Allen was briefly backed up by local vending machine worker Tyler Stewart after regular backup Carter Hutton was injured at the morning skate.
Dallas has lost two in a row since a season-high five game winning streak. Kari Lehtonen stopped 24 shots.
The Blues scored twice on the power play after connecting on just 2 of 17 chances in their previous four games. Schenn, acquired in an offseason trade with Philadelphia, pounced on a rebound from close range midway through the first period for a 1-0 lead.
“It was good to get a couple, but the execution can still be better,” Schenn said. “We had a lot of chances, but at the end of the day we got two and we’ll keep working at it.”
Parayko blasted a shot from just inside the blue line that eluded Lehtonen early in the third period.
Tarasenko scored into an empty net with 47.6 seconds left, ending a six-game scoreless streak.
Dallas is 0-6 against the top three teams in the Central Division — St. Louis, Winnipeg and Nashville. The Stars have been outscored 25-8.
“We’re not happy with it,” Dallas winger Alexander Radulov said. “We just have to figure it out and win these games — it’s important.”
The Stars committed seven penalties.
“We took the penalties because we were second place to the puck,” coach Ken Hitchcock said. “We got beat to a lot of those races.”
NOTES: Stewart participated in warmups and backed up during the first period while St. Louis waited for G Ville Husso to arrive from San Antonio of the AHL. “I’m sure it was pretty exciting for him,” Allen said. “It’s great to see guys get chances like that.” Husso got to the rink late in the first period. … Hutton has a lower-body injury. … Dallas G Ben Bishop missed the game and remained in Dallas with a sore back. Coach Ken Hitchcock said Bishop could be ready for Saturday’s home game against Vegas. … Stars LW Antoine Roussel missed his fourth straight game with the flu.