ST. LOUIS -- St. Louis Blues coach Ken Hitchcock was searching for whatever line combinations would work against the Montreal Canadiens before it was too late.
The Blues had nothing going down 2-0 in the third period but then Hitchcock put forwards Jaden Schwartz and Paul Stastny together and it gave St. Louis a spark.
Schwartz scored twice, including the game-winning goal with 1:22 left in overtime to give the Blues a 3-2 victory against the Canadiens at Scottrade Center on Tuesday.
WATCH: All Canadiens vs. Blues highlights
Schwartz took a pass from Alexander Steen and beat Al Montoya high glove side to give the Blues (15-7-4) their third win of the season (3-5-1) when trailing after two periods.
"[Steen], I think he won the battle in the 'D' zone," Schwartz said. "They might have had a couple of tired guys out and he took off. I went with him and I think the defensemen were cheating his way a little bit and he made a great pass over a couple of sticks and it landed on my tape. I had a little bit of a step on the defenseman there. He was leaning down a little bit, so I just tried to get it up as quick as I could."
Video: MTL@STL: Stastny feeds Schwartz to tie the game
Schwartz had three points and Paul Stastny had a goal and an assist for St. Louis. Jake Allen made 28 saves and is 8-0-0 in his past eight starts; he's 10-0-2 at home this season. The Blues have points in 13 straight home games (10-0-3) and are 12-1-3 at Scottrade Center.
"I was trying a lot of stuff once it wasn't working, and then I saw some things in the second period I liked," Hitchcock said. "A couple shifts and after the first three minutes ... they had a great shift with about five minutes gone in the third period and I just stuck on those lines."
Tomas Plekanec and Paul Byron each had a goal and an assist, and Montoya made 28 saves for the Canadiens (17-6-3), who finished a five-game road trip 2-2-1. Montreal is 4-5-2 in its past 11 after starting 13-1-1.
"I've got to look at the big picture," Canadiens coach Michel Therrien said. "I thought we were pursuing the puck really well. We got some good scoring chances, especially in the second period. We hit two posts and the first goal in the third gave them some momentum, but you know what, we've got to be satisfied. Disappointed losing the game obviously, but we played against a really good hockey team."
Video: MTL@STL: Byron tips home PPG to open the scoring
The Blues ended Montoya's shutout 7:40 into the third when Stastny scored on a shot from the left circle short side to make it 2-1.
Schwartz tied it at 10:31. Jay Bouwmeester's shot from the left point was loose and Schwartz scored on the rebound after Stastny's backhand attempt.
Allen was unable to handle Plekanec's shot from the left circle. Byron got a piece of it and the puck caromed off defenseman Carl Gunnarsson's skate and between Allen's pads to give Montreal a 1-0 lead at 10:06 of the first period.
The Blues failed to convert on three power plays in the first.
Plekanec scored his first in 14 games after receiving a saucer pass from Byron in the slot and beating Allen with a backhand shot high glove side with 2:18 remaining in the second for a 2-0 lead.
Video: MTL@STL: Allen stonewalls Danault to keep game tied
Goal of the game
Stastny's goal came after Blues defenseman Colton Parayko kept Jeff Petry's clearing attempt in the zone. A strong forecheck in which Stastny and Schwartz won a puck battle with Petry gave Stastny a small shooting lane that he scored over Montoya.
Video: MTL@STL: Stastny picks the corner to beat Montoya
Save of the game
Allen made a quick left-pad save on Canadiens captain Max Pacioretty's redirection off a Plekanec pass with 1:18 remaining in regulation.
Video: MTL@STL: Allen denies Pacioretty to preserve tie late
Highlight of the game
Plekanec and Byron broke out of their zone on a 2-on-1. Byron's slick saucer pass to Plekanec set up a backhand shot past Allen.
Video: MTL@STL: Plekanec backhands Byron's dish top shelf
Unsung moment of the game
Schwartz may have scored the game-winning goal, but Steen did most of the work, first winning the puck from Canadiens forward Andrew Shaw behind the Blues net and then threading a pass in stride to Schwartz going in on goal through three Canadiens.
Video: MTL@STL: Schwartz roofs overtime winner past Montoya
They said it
"It would have been nice to get two [points], but we battled hard and they got a little bit of life there. I thought we battled to the end." -- Canadiens captain Max Pacioretty
"That's a good win for us, especially against the No. 1 team in the League. It's good momentum to go on this road trip." -- Blues goalie Jake Allen
Need to know
Canadiens center David Desharnais left the game in the third period because of a lower-body injury and did not return. Montreal learned Monday that center Alex Galchenyuk is out indefinitely because of a lower-body injury. ... Schwartz has seven goals and five assists in his past 10 games.
Canadiens: Host the New Jersey Devils on Thursday (7:30 p.m. ET; SN360, RDS, MSG+ 2, NHL.TV)
Blues: At the New York Islanders on Thursday (7 p.m. ET; MSG+, FS-MW, NHL.TV)
Video: Schwartz, Blues come back to edge Habs in overtime