Steen's drive with 21.1 seconds left trickled through Crawford and lifted the Blues to a 3-2 victory against the defending Stanley Cup champions on Wednesday night.
Steen broke down the left side as part of a 3-on-1 rush. Instead of passing, he let go a shot from just inside the left circle.
"You pick a spot," Steen said. "I don't know that it's really how hard it is. It's more where you put it."
The Blackhawks (1-1-1) lost for the first time in regulation. Chicago coach Joel Quenneville was particularly upset that his team gave up an odd-man break so late in a tie game.
"You've got to get that game to overtime," Quenneville said. "You take one (point) maybe two. You don't get none. That's unacceptable.
"There was not a lot of mistakes. We played a good game. But you can't make a mistake like that."
The Blues (3-0) matched their best start to a season, also done in the 1969-70 and 1993-94 campaigns.
"Playing Chicago is always a big game," Blues goalie Jaroslav Halak said. "I think our guys came up big. We stuck to the game plan and didn't give up."
Halak, who made 26 saves, has been in net for all three wins.
"You just have to focus on every shot and try not to give up rebounds," Halak said.
Tarasenko gave the Blues a 1-0 lead when he beat Crawford with a wrist shot from the slot with 4:16 left in the first period.
Kane tied it with a power-play goal 1:17 later. Patrick Sharp's shot from the right circle trickled through to Kane at the left post, and he swatted the puck in.
In the second period, Backes put the Blues back in front at 8:37 when he redirected Alex Pietrangelo's shot from the right point into the net. But after Jaden Schwartz went off for hooking, Toews tied it 39 seconds later when he shoved a rebound past Halak.
NOTES: Kane's power-play goal was the first allowed by the Blues in 12 chances this season. The goal also ended Halak's shutout streak at 111 minutes, 52 seconds. ... The game featured a matchup of the two most successful coaches in Blues history. Current St. Louis coach Ken Hitchcock entered with the best winning percentage of .676 (74-32-13). Quenneville is second at .598 (307-191-95).