Brenden Morrow added a power-play goal midway through the third period and Maxim Lapierre scored into an empty net with 2:08 left. The Blues have won three straight and moved a point ahead of the Blackhawks, who played later at Calgary, for the Central Division lead.
The Blues cleaned up on defence a week after getting whipped 7-1 in New Jersey when Halak surrendered four goals in 14 shots after relieving Brian Elliott. Halak has started all three games since that setback, allowing a total of four goals.
The Devils mustered little offensively three days after losing 7-3 to the Rangers at Yankee Stadium. They were shut out for the sixth time, although this was the first time in 35 games.
The Blues are an NHL-best 17-3-1 against the Eastern Conference, and 9-0 at home.
Steen was the NHL's second-leading goal scorer in late December before missing 11 games with a concussion. He's been back six games and has a point in the last five with three goals and four assists.
Halak and Brian Elliott have combined for seven shutouts this season. Halak has won four straight starts with two shutouts this month, and holds the franchise mark with 20 shutouts in four seasons.
St. Louis killed off Roman Polak's high-sticking penalty just nine seconds into the game, and then took the lead on Steen's 27th goal at 3:25. Steen scored his 100th goal in six seasons with St. Louis scoring from the slot on an odd-man rush with assists by Jaden Schwartz and David Backes.
Alex Pietrangelo took a holding call foiling a break-in by Stephen Gionta late in the period and, again, the St. Louis penalty killers came through. The Blues' Vladimir Sobotka hit the goal post on an odd-man rush with just under five minutes to go.
The Devils played in St. Louis for the first time since Nov. 20, 2010, a 3-2 Blues victory.
NOTES: NFL Hall of Famer Dan Dierdorf, who recently retired from broadcasting, wore a Blues jersey with his number 72 while watching from a private box. ... New Jersey is 5-16-3 when trailing after two periods. ... Jaromir Jagr had totalled two goals and four assists the previous four games.