DETROIT -- As he took the ice for Monday's game against the Montreal Canadiens, Jared Coreau did his best not to think about the fact that the goalie at the other end of the ice was his idol.

"I look down and I know it's him, but at the end of the day whether it's Carey Price or another goalie -- if it's a breakaway from Sidney Crosby or any other player -- we still have to score goals and I still have to save shots," Coreau said. "So you try not to think about it too much. If you think about something too much or one player it'll consume you and distract you from the big picture.

When all was said and done, Coreau matched his idol save for save and beat him.

Playing in just his eighth NHL game, Coreau made 18 saves for his second shutout as the Detroit Red Wings bested former Hart and Vezina Trophy winner Price and the Canadiens 1-0.

Coupled with Saturday's 6-3 win over the reigning Stanley Cup champion Pittsburgh Penguins, it's the first time Detroit has won back-to-back home games since Oct. 22-25.

"We've talked for a while here that we need to tighten it up defensively and I thought we were real solid defensively most of the game," Detroit coach Jeff Blashill said. "I thought all six D played really, really well."

Coreau improved to 5-1-1 since his Nov. 26 recall from Grand Rapids of the American Hockey League.

"He played very well tonight," Price said. "He's a big body. He fills up a lot of net and keeps his game simple, quiet. I'm sure his coaches like that."

Thomas Vanek scored the only goal late in the second period. Jousting in front of the Montreal net with Canadiens defenseman Jeff Petry, Vanek extended his scoring streak to six games when Danny DeKeyser's point shot banked off Vanek's leg and past Price at 18:46. Vanek has recorded five goals and four assists during his point streak.

"They did a pretty good job of getting that high guy in the slot," Price said. "Their D men were looking for that and they missed a really good chance right off the get go.

"They've got some guys in front that are really good with their sticks and seeing pucks and tipping them."

Vanek missed two golden scoring chances earlier in the period during a Detroit power play. He deflected a shot behind Price but it skidded directly across the goal crease and harmlessly out the other side. Seconds later, Price made a right pad save on a point-blank drive by Vanek.

"I've played with Pricer and he's the best goalie in the world," Vanek said. "There's not too many point-blank shots that are going to go in on him. It's going to have to be those shot tips and those ugly goals in front of the net and redirections."

In the first period, Price sprawled to make a spectacular glove save and rob speedy Detroit forward Andreas Athanasiou on a breakaway chance.

"I wish we could have generated more offense," said Montreal coach Michel Therrien, whose team held the opposition to less than three goals for the first time in seven games but was held to one goal or fewer for the third time in five games.

"I thought we tied them up defensively, which is something we worked on yesterday, and Carey was very good. We just didn't get any puck luck -- they had a goal go in off a pad and we had our shots bounce past the post.

Coreau wasn't as busy as Price in terms of high-end chances. His best stop was a blocker save in the second period after Canadiens captain Max Pacioretty set up Alex Galchenyuk for a one-timer off a Detroit turnover.

NOTES: Detroit G Jimmy Howard, on injured reserve due to a knee injury, skated on his own for the first time Monday. ... Detroit held Montreal to 18 shots, a season low, ... Vanek leads the Red Wings with 12 goals and has been held off the scoresheet just three times since Dec. 1. ... Detroit scratches were Fs Tomas Jurco and Steve Ott and D Ryan Sproul. F Darren Helm (shoulder) and Ds Brendan Smith (knee) and Niklas Kronwall (groin) are also on the IR. ... LW Jacob De La Rose, recalled Sunday from AHL St. John's, made his season debut for Montreal. ... The next goal by Canadiens F Tomas Plekanec will be his 223rd for Montreal, tying him with Peter Mahovlich for 18th on the club's all-time list. ... Canadiens scratches were forwards Michael McCarron and Daniel Carr and defenseman Ryan Johnston. Fs David Desharnais (knee) and Brendan Gallagher (hand) and Ds Andrei Markov (lower body) and Greg Pateryn (ankle) are on IR.