''It's a good week,'' Binnington said after his sixth NHL game.
He made 21 saves on Saturday, the first time he has started consecutive games.
''(Binnington)'s been amazing,'' Tarasenko said. ''Plays really confident. He gives us a lot of confidence, too.''
Pat Maroon also scored for the Blues, who have won two straight for the fifth time this season.
''I hate to use the word desperate times,'' St. Louis interim coach Craig Berube said, ''but we've got to win games. They're in our division, and we're trying to catch them.''
Tarasenko scored in the first minute and Maroon added a first-period goal against Bishop, who won 3-1 at St. Louis four nights earlier. Veteran Jake Allen was in goal for the Blues in that game.
''We've got to be ready when the puck is dropped,'' Stars defenseman John Klingberg said.
Binnington said the Blues' fast start was a great help to him.
''That's two games in a row we've had a couple of goals in the first period, and that helps everyone to feed off that. From there on, we just play our game, keep it simple.''
Condra broke up Binnington's chance for a second shutout, scoring his first goal with Dallas at 8:35 of the third period.
''(Binnington)'s confident and he's aggressive,'' Berube said. ''He looks pretty calm and cool in there.''
The Stars have lost three of four, but are in third place in the Central Division.
Tarasenko scored on the first shot of the game, 34 seconds in, from the right faceoff circle. Maroon's backhand from the right of the net extended the Blues' lead to 2-0 at 9:54.
Dallas had a scoring chance midway through the second period, but Jason Spezza's wrist shot from the top of the slot went over Binnington's shoulder and off the crossbar.
''It sounded like a post,'' Binnington said. ''Luckily for me it didn't go in the net.''
Spezza said the shot was frustrating when the Stars were trying to come back.
''You like to see those ones go in to get some momentum,'' he said.
In the third, a shot blocked in front went to Condra at the right of the net and he scored on a short wrist shot. St. Louis challenged the goal looking for goaltender interference, but the goal stood.
Tarasenko scored his second goal on the power play at 12:38. Oskar Sundqvist picked up his second assist of the game.
''It was a big play by a big player,'' Binnington said. ''He's an elite guy, an elite shot, and it was an important time for us to get a goal.''
NOTES: Tarasenko has 15 career goals against Dallas. He also has seven assists for 22 points in 25 games. Over the last five seasons, he is tied with Winnipeg's Patrik Laine for the most goals (14) vs. the Stars over the last five seasons. . Binnington was leading the AHL with a 2.08 goals against percentage when he was promoted from San Antonio. . The win improved the Blues' record under interim coach Craig Berube to 12-12-1. . Condra was playing in his fifth game since being promoted from Texas of the AHL. His 40th NHL goal was his first since April 7, 2016. . Dallas D John Klingberg assisted on Condra's goal and he has five points (one goal, four assists) in the last four games.
Blues: Visit Washington on Monday for the second game of a four-game trip.
Stars: Host Tampa Bay on Tuesday in the second of a six-game homestand.
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