The Blues evened their early-season record at 2-2 and San Jose lost for the second time in three games.
The Sharks took a 2-1 lead into the third period, having gone in front on a slap shot by Brent Burns that found the net with 8:42 to go in the second.
Huskins tied it 4:33 into the third and Steen scored his second of the season less than 5 minutes later to put the Blues in front. David Backes scored into an empty net with 27 seconds left.
Brian Elliott, starting his first game of the year, collected the victory by making 34 saves. Thomas Greiss, filling in for the Sharks while Antti Niemi recovers from a knee injury, gave up three of the four St. Louis goals on 22 shots.