Steen broke down the left side as part of a 3-on-1 rush. He kept the puck and let go a drive from just inside the circle that trickled through Crawford.
The Blues (3-0) matched their best start to a season, also done in the 1969-70 and 1993-94 campaigns. Jaroslav Halak made 26 saves in his third straight win. Vladimir Tarasenko and David Backes also scored for St. Louis.
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). Chicago's Joel Quenneville is second at .598 (307-191-95).