DETROIT -- Thomas Vanek scored late in the second period and Jared Coreau earned his second shutout, leading the Detroit Red Wings to a 1-0 win over the Montreal Canadiens on Monday.

Detroit won consecutive games at home for the first time since starting the season 4-0 at Joe Louis Arena as part of its 6-2 start. The Red Wings began the day in last place in the Atlantic Division.

The Atlantic Division-leading Canadiens had won five of their last seven games.

The 6-foot-6 Coreau, the tallest goaltender to play for the Red Wings, stopped 18 shots to improve to 5-1-1 in his first season with Detroit. He signed with the team in 2013 and played in the minors until getting a chance recently because Jimmy Howard is on injured reserve and Petr Mrazek is struggling.

Montreal star Carey Price made a spectacular save late in the first period, using his glove to deny Andreas Athanasiou on a breakaway, and finished with 19 stops. Price, who has lost six of his last nine starts, has a losing record since starting 10-0 this season.

Vanek extended his point streak to a season-high six games, redirecting Danny DeKeyser's shot past Price with 1:36 left in the second. The veteran stood in front of the net, obstructing Price's vision as he competed for position with Montreal defenceman Alexei Emelin.

The 32-year-old Vanek has a team-high 12 goals and is averaging almost a point per game in his first season with the Red Wings. They signed him to a $2.6 million, one-year deal after he had 41 points in 73 games last year with the Minnesota Wild.