The victory moves the Red Wings within one win of tying the NHL record of 20 successive home victories set by Boston in 1929-30 and matched by Philadelphia in 1976. Detroit's next home game is on Sunday against the Flyers.
Todd Bertuzzi scored the shootout winner with a backhand to the top corner and third string goalie Joey MacDonald, who was stellar in the later stages of the game, turned aside Bobby Ryan's attempt to secure the win.
"Eighteen straight and you're in a shootout and you know you have three shooters," MacDonald said.
"We scored. Pav (Pavel Datsyuk) got a nice one and when Bert (Todd Bertuzzi) got that one, it put a little more pressure on me. I didn't want to go into any extra shooters. I just tried to stay out and stay big and made the save."
Ducks winger George Parros scored his first goal of the season late in the first period but the lead was short-lived as Detroit's Justin Abdelkader leveled the score less than three minutes later tipping a shot by defenseman Jakub Kindl past Ducks goalie Jonas Hiller.
The Ducks thought they had regained the lead through Niklas Hagman in the second period, however, the goal was waived off because Parros was deemed to have shoved Tomas Holmstrom into MacDonald and was assessed a minor penalty on the play.
In a penalty-filled overtime period, Ducks defenseman Cam Fowler nearly ended the streak as he slipped behind the Detroit defense and beat MacDonald with a fake to the backhand only to hit the post.
MacDonald, recalled from the minors on February 3 and playing in his fourth game of the season, made 14 of his 30 saves in the third period and overtime to force the game to the shootout.
"I thought his (MacDonald) game tonight was the best," Red Wings coach Mike Babcock said.
"We haven't needed him like we did tonight. But I thought today he was big and square and out and confident. He looked like a real goaltender for us. So that's a real positive for us."
Both teams hit the goalposts on several occasions and neither could convert on the powerplay. The Red Wings were unsuccessful on six powerplays while the Ducks went 0-for-7 with the man advantage.
"We think we certainly deserve a better fate," Ducks coach Bruce Boudreau said. "But when you go 0-for-7 on the powerplay, even if you have three great looks, or four great looks and you don't score, you don't expect to win."