Todd Bertuzzi supplied the decisive goal in the 1, to push their franchise-record home winning streak to 19 games.
Following an exciting overtime, Bertuzzi skated in on Jonas Hiller very slowly and beat the Anaheim goaltender with a backhander. Joey MacDonald then denied Bobby Ryan to assure the extra point for NHL-leading Detroit, which hasn't lost at Joe Louis Arena since November 3 against Calgary.
The Red Wings' current string of home victories is the longest in the NHL since the Philadelphia Flyers tied the league record by winning 20 in a row during the 1975-76 season. The mark was first set by the 1929-30 Boston Bruins.
"We know it's a grind and not easy, but when you're playing well, especially at home, you just keep going with it and try not to think too much about it," said Detroit defenseman Nicklas Lidstrom.
MacDonald made 29 saves for the Red Wings, who pace the NHL with 76 points.
Hiller stopped 23 shots for Anaheim, which has lost eight straight at Detroit.
"We think we deserved a better fate," said Anaheim head coach Bruce Boudreau. "But when you go 0-for-7 on the power play, you make things a lot tougher on yourself."
The Ducks had a great opportunity to snap their skid in overtime, but defenseman Cam Fowler hit the post on a breakaway as the teams skated 3-on-3. Detroit countered with a rush the other way and it led to Corey Perry taking a tripping penalty with 54 seconds remaining. The Red Wings wound up with a two- man advantage, but couldn't convert.
Anaheim and Detroit traded goals in the first period.
Ducks enforcer George Parros opened the scoring when he redirected Rod Pelley's shot with his right skate at 16:17. It was his first goal since December 1, 2010.
Justin Abdelkader got his stick on Jakub Kindl's shot from the blueline, tying the game at 18:42.
Lidstrom matched Alex Delvecchio (1,549) for second place on the Red Wings' all-time games played list...Detroit's Tomas Holmstrom suited up for the 1,000th game of his career. He became the 272nd player in league history to reach that figure and just the sixth to skate in 1,000 games with the Red Wings...Anaheim opened an eight-game road trip, equaling the longest uninterrupted swing in club history...Red Wings forward Danny Cleary missed Friday's game following a procedure to drain fluid from behind his left knee.