Detroit's Jimmy Howard made 27 saves for his fifth shutout this season and NHL-high 27th victory.
The Sabres have lost a franchise-record nine straight road games in regulation.
Buffalo goalie Ryan Miller was pulled early in the second after giving up goals to Zetterberg, Johan Franzen, Nicklas Lidstrom, Todd Bertuzzi and Darren Helm.
The Red Wings improved to 18-2-1 at Joe Louis Arena, where they haven't lost since Nov. 3, 2011, when Calgary beat them, 4-1.
In other games *
At Uniondale, N.Y., Sergei Kostitsyn and Matt Halischuk scored on Nashville's first two shots as the Predators rolled to a 3-1 victory over the New York Islanders.
* At Glendale, Ariz., Shane Doan and Boyd Gordon scored two goals each and the Phoenix Coyotes returned from an 0-3 road trip to rout the Colorado Avalanche, 6-1.
* At Ottawa, Chris Mason made 25 saves for his second shutout and the Winnipeg Jets ended a three-game losing streak with a 2-0 win over the Senators.
Jim Slater and Tobias Enstrom scored for the Jets, who had lost five of six.
* At St. Louis, T.J. Oshie scored in the third period and Jaroslav Halak had 22 saves as the Blues defeated the Dallas Stars, 1-0.
Before the game, the Stars placed center Mike Ribeiro on injured reserve with a lower-body injury.
* At Sunrise, Fla., Patrice Bergeron scored two goals and David Krejci scored the winner in the shootout and the Boston Bruins beat the Florida Panthers, 3-2.
Bergeron scored two goals for Boston, and Tuukka Rask stopped 38 shots.
Noteworthy *
Columbus forward Dane Byers was suspended three games without pay for a shoulder-to-head hit on San Jose's Andrew Desjardins on Saturday. Under the terms of the collective bargaining agreement, and based on his average annual salary, Byers will forfeit $8,918.91. The money goes to the Players' Emergency Assistance Fund. Desjardins was helped off the ice and did not return. He also did not play in the Sharks' game Sunday against Chicago.
* Pittsburgh's Sidney Crosby will meet with a specialist this week because of lingering concussionlike symptoms.
He hasn't played since Dec. 5 following a recurrence of the symptoms that sidelined him for more than 10 months last year. The team says Crosby will work with chiropractic neurologist Dr. Ted Carrick, who treated Crosby for similar symptoms last summer. There is no timetable for Crosby's return.
* Washington defenseman Mike Green will have abdominal surgery and is expected to be sidelined 4 to 6 weeks.