Tarasenko's goals broke a 1-1 tie and helped send the 46,556 fans home happy.
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Patrik Berglund scored in the second period for the Blues (20-13-5) and Alexander Steen scored an empty-net goal with 1:14 remaining. Jake Allen made 22 saves.
"I don't know about [my teammates], but it's probably the coolest thing I've been a part of," Blues captain Alex Pietrangelo said.
The threat of rain delaying the game was omnipresent, but aside from a few sprinkles, precipitation never proved to be a problem.
The game started on time and finished in two hours and 27 minutes. The rain that did fall couldn't dampen the party; fans roared from the anthem past the buzzer. The temperature at opening faceoff was 46.7 degrees Fahrenheit.
"All things considered, we lucked out with the weather," Blues defenseman Kevin Shattenkirk said. "The ice was a little bumpy and it was a little slow. But really, for us, it was fine. That's something we just adjust to and we simplified our game and I think that's why we were so effective out there tonight. Especially after all the warnings and what we thought was coming, we were pretty lucky to be able to get that game in."
Tarasenko's first goal, the game-winner at 12:05 of the third period, was a pass attempt to Jori Lehtera that banked off Blackhawks defenseman Niklas Hjalmarsson's skate and into the net.