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MONTREAL -- The Buffalo Sabres made the right call when they finally gave Ryan Miller a night off, bringing up a shootout specialist from the minors to start in goal over their very idle backup.

Rookie goalie Jhonas Enroth stopped seven of Montreal's final eight shooters in the tiebreaker and Jochen Hecht scored on Buffalo's 10th attempt to give the Sabres a 3-2 win over the Montreal Canadiens on Tuesday night.

Buffalo won the shootout 4-3 as the teams matched the NHL record for most goals in a shootout.

Enroth, who was already the first goalie in league history to get his first two wins in shootouts, made 32 saves during the game, his first with the Sabres since Nov. 24, when he had 28 saves in a 1-0 loss to the Pittsburgh Penguins.

"I think I'm pretty good at shootouts, but I don't know, first three wins in the shootout is pretty unique," said Enroth, whose wins have all come on the road.

Miller was rested and did not dress, ending his streak of 31 consecutive starts.

"Ryan plays a lot of games," said Jason Pominville, who tied it at 2 for Buffalo with his 13th goal 6:08 into the third. "He wants to play every game. He's a competitor and he wants to be out there and help this team, but at the same time we're all aware that he needs rest and hopefully it will help him out and at the end of the day just benefit the team."

The win gave the Sabres a 13-5-2 record since top scorer Derek Roy was lost for the season with a knee injury. Buffalo moved within two points of the Carolina Hurricanes for the eighth and final playoff spot in the Eastern Conference going into a home game Wednesday night against the Toronto Maple Leafs.

Enroth, recalled from AHL Portland earlier in the day, got the nod over Patrick Lalime, who has been limited to just two relief appearances since his last start on Nov. 20.

"I thought he did a great job," Sabres coach Lindy Ruff said. "That's the reason that he's been down there trying to develop and playing games, and the reason he's here is because of how hard he worked in Portland. We knew that it was going to get to a point where he was going to get an opportunity to play and he came up and proved that he can be a capable NHL goaltender."

Ruff said no decision had been made on whether Enroth would remain with the team.

"We'll discuss that on the plane," Ruff said.

Drew Stafford got his ninth goal in five games late in the second to bring the Sabres within 2-1. His power-play effort snapped Carey Price's shutout streak at 102 minutes, 54 seconds.

Stafford leads the team with 24 goals, including 19 in his last 22 games. He recorded his fourth hat trick of the season, his second in three games, in Sunday's 7-6 overtime loss to the New York Islanders.

Stafford failed to score on the Sabres' first shootout attempt. Needing to convert each of the next two, Buffalo got goals from Thomas Vanek and Tyler Ennis before Price turned aside five of the next six shooters.

"It's tough when it's going that long," Canadiens captain Brian Gionta said. "It's a big point at hand and I thought Carey did a great job."

Price, who recorded his sixth shutout of the season in a 3-0 win over Toronto on Saturday, made 30 saves. Before Stafford scored, he had not allowed a goal since he was beaten a career-high eight times in a wild, fight-filled 8-6 loss in Boston on Wednesday.

Max Pacioretty scored a power-play goal in the first and Benoit Pouliot put Montreal up 2-0 with his 13th goal 6:28 into the second.

Montreal was on the power play for the first 36 seconds of overtime after Buffalo's Mike Weber was called for tripping late in the third.

Pacioretty, who put a shot off the left post on a power play early in the third, extended his points streak to five games when he opened the scoring 4:54 in. The 22-year-old left wing scored his fourth goal in as many games when he jammed home his own rebound after he took Tomas Plekanec's pass to the right of the goal and drove to the net.

Pouliot made it a two-goal lead when he finished off David Desharnais' pass after the rookie center drove into the Sabres' end after taking defenseman James Wisniewski's feed up the middle.

"We put ourselves in a pretty bad spot," Ruff said. "We didn't play a very good first period. I thought we really went to work in the last 45 minutes. Even the late penalty kill was something that was really important."

Brendon Nash made his NHL debut for the Canadiens, who called up the 23-year-old defenseman from AHL Hamilton earlier in the day. Jaroslav Spacek did not play because of a lower-body injury.

Game notes

Miller went 18-9-3 with three shutouts during his streak, from Nov. 26 through Sunday. ... Lalime has lost each of his four starts this season. He is 0-5 in seven games. ... Sabres center Tim Connolly, who assisted on Stafford's goal, played his 600th game. ... Canadiens left winger Mathieu Darche returned after missing two games because of a lower-body injury. Defenseman Hal Gill missed his third game in a row because of an upper-body injury. ... Left winger Lars Eller did not dress for Montreal. ... Canadiens left winger Travis Moen played his 500th game.