Henrik Zetterberg had a goal and two assists, and goalie Ty Conklin made 24 saves for Detroit in his 11th straight home victory.
Pavel Datsyuk added a goal and an assist, and Dan Cleary, Johan Franzen and Kris Draper also scored for the Stanley Cup champions.
Ryan Getzlaf and Bobby Ryan got the goals for Anaheim, which lost its third straight and missed a chance to move up to eighth and a provisional playoff berth in the West.
Datsyuk's power-play goal with 33 seconds left in the opening period put Detroit up 2-1, set up by Zetterberg. Dastsyuk returned the favor in the second period, setting up the Swede to make it 3-1 and put the Red Wings in control.
Avalanche 4, Capitals 1
In Washington, Colorado won its third straight to give coach Tony Granato his 100th career victory and beat Washington.
The Avalanche also ended Washington's winning streak at three, and snapped Alex Ovechkin's points streak at 10 games.
The win lifted Colorado out of outright last in the Western Conference while the Capitals missed a chance to go clear second in the East.
Hurricanes 4, Lightning 1
Joe Corvo scored two 5-on-3 goals 39 seconds apart for Carolina, and Jussi Jokinen scored the go-ahead goal against his former team.
Carolina moved to ninth in the East, a point behind Florida and Buffalo in the race for the final playoff spot.
The Lightning had a season-worst one shot on goal in the first period and lost for the fourth time in seven days.