Dallas coach Lindy Ruff agreed, "He made the saves that kept them in the game."
Brenden Dillon scored for Dallas, which fell to 8-6 on the road.
Elliott says the key to his success as a backup comes from his mental preparation.
"You just trust in your game and everything else will take care of itself," he said. "When you don't get a lot of opportunities, it's hard to get in that peak performance state. I think it just comes with experience and a lot of patience."
Tarasenko put the Blues ahead to stay with his eighth goal of the season at 11:02 of the first period, just 9 seconds after the Stars had tied it 1-all.
Backes pushed the lead to 3-1 by converting on a two-on-one. Backes, using
Jaden Schwartz as a screen, held the puck before beating goalie
Kari Lehtonen, who was pulled in the third period after allowing five goals on 18 shots.
The Blues' balanced four-line attack did a good job taking advantage of limited opportunities. St. Louis had 25 shots on goal.
"Through the whole lineup everybody was solid," Oshie said. "When we can go at them in waves, I think that's when we're at our best."
The Stars were coming off a season-high 43 shots in a 3-2 loss to the New York Rangers.
They managed to create numerous opportunities on Saturday, but could not solve Elliott.
"It might be the most misleading 6-1 game I've ever been in," Ruff said. "For the most part, we outskated them and in a lot of areas we outworked them."
Lehtonen took full blame for the loss,
"I had a bad night," he said. "I feel bad for the guys. They tried hard."
Sobotka scored 1:39 into the game for his 100th career point.
St. Louis RW
Ryan Reaves broke his right hand in a first-period fight with Dillon and will
be out up to four weeks.
NOTES: This was first of five meetings between the new Central Division rivals. ... Dallas LW Ray Whitney missed his fifth successive game with a groin injury. ... Stars C
Cody Eakin played in his 100th game. ... St. Louis is 11-2-1 in its last 14 contests. ... Blues LW Brenden Morrow, who spent 13 seasons with Dallas, picked up an assist on Stewart's goal and now has a point against every NHL team.