Oshie beat Carey Price in the shootout, and the Blues won 3-2 on Tuesday night for their fourth consecutive victory against the Canadiens.
"(Price) is a great goaltender," Oshie said. "He's proven that. We were just trying to get shots through any way that we could. And when they did get through, it seemed as though he was a wall back there.
"He was good in the shootout as well. I think I got a little lucky. I just tried to flip it upstairs."
The Canadiens had no shots in overtime.
"We didn't have a good first pass coming out of our own end," captain Brian Gionta said. "The crowd got frustrated a little bit there.
"We didn't get anything going."
Tomas Plekanec had a chance to win it in regulation for Montreal. He was awarded a penalty shot in the final minute but missed the net high and wide.
"Half an inch on either side, and it's a goal," Plekanec said. "It's hard to say I would do anything different on that one."
St. Louis opened the scoring at 2:38 of the first period when Steen collected his NHL-best 13th goal of the season.
Blues captain David Backes got it started by stealing the puck from defender Douglas Murray, who was playing softly behind his own net. Backes pushed Murray down and passed the puck to a wide-open Steen, who beat Price over his left shoulder.
Montreal tied it at 5:38 of the second period. Andrei Markov drove hard to the net, colliding with Halak in the process. With Halak still shaken up, the puck fell to Bourque in the crease, and he converted from in close.
Bournival put the Canadiens in front at 14:49 with his fourth of the season. He intercepted a poor pass from Jay Bouwmeester in the St. Louis zone and quickly fired a slap shot between Halak's legs.
"I want to help the team as best as I can," Bournival said. "That's my mandate here. I want to create things offensively, apply myself defensively, try to win pucks along the boards. That's what I'm concentrating on."
Stewart tied it again at 10:31 of the third period when he deflected a Kevin Shattenkirk blue-line shot off the post and past Price.
"Stewart was one of our best forwards," Blues coach Ken Hitchcock. "He was competitive, hard on the puck, dangerous offensively. It didn't matter where we played him. If this is the level he's going to play with, it's a good level."
Halak returned to Montreal for the second time since being traded to the Blues in 2010. He earned a shutout in his other trip to Montreal in January 2012, winning 3-0.
David Desharnais was out of the Canadiens' lineup after a slow start to his season. The 27-year-old forward, who recently signed a four-year contract extension, has one point in 15 games this season.
The Canadiens were coming off back-to-back road losses to the Wild and Avalanche. ... Montreal was without injured players Daniel Briere, Brandon Prust, Alexei Emelin and Travis Moen. There is no timetable yet for their return.