Tomas Holmstrom scored with 4:54 left in regulation on a shot that hit him standing in front of goalie Jean-Sebastien Giguere before hitting the ice and trickling into the net, giving Detroit a 2-1 victory Friday night.
"We had traffic and it was a good goal," Red Wings coach Mike Babcock said.
Henrik Zetterberg's shot deflected off a Duck and got past Giguere at 3:44 of the first period and Detroit held on to the lead for nearly two periods.
Both of Detroit's goals were last touched by Anaheim defenseman Francois Beauchemin.
"That's a freak thing that happens and it happened to us," Ducks coach Randy Carlyle said. "We'll move on."
Game 2 is Sunday night in Detroit before the series shifts to Anaheim.
Chris Kunitz made it 1-all early in the third period with a shot from the slot that beat Dominik Hasek on the glove side. It was the first goal Hasek gave up in nearly 157 minutes.
With two stellar goaltenders and four Norris Trophy winners - combining to be honored as the NHL's top defenseman nine times - it was a low-scoring game as expected.
Shortly after Holmstrom's goal, Anaheim had a chance to tie it again on a power play and the Ducks pulled Giguere to make it a two-man advantage, but they couldn't score.
Hasek made 31 saves and Giguere stopped 17 shots.
"Dom was outstanding," Babcock said. "Dom shut the door."
The Western Conference's first- and second-seeded teams won their first two series a year after the conference's top four teams lost in the first round.
Anaheim is in the conference finals for the third time in four postseasons, more than any team since 2003. Detroit, meanwhile, is among the final four in the league for the first time since winning the Stanley Cup in 2002.
The Red Wings and Ducks are matched up for the fourth time in the playoffs - and Detroit is hoping it can continue a trend.
Each of the previous three meetings have ended with sweeps, with the Red Wings winning in 1997 and 1999, and Anaheim advancing past them in 2003 with Babcock behind its bench.
It took just 8 seconds in Game 1 for Detroit to score against the Ducks' vaunted penalty-killing unit. Zetterberg won a faceoff, got the puck back along the left boards and his shot from the bottom of the right circle hit Beauchemin and was redirected between Giguere's pads. Anaheim allowed just three goals on 56 power plays during the first two rounds, leading to an NHL-high 94.6 percent success rate on penalty killing. While the Red Wings took advantage of their only power play in the opening period, Anaheim went 0-for-3 and only took one shot with a two-man advantage for 1Â½ minutes shortly after Detroit scored. "Those things come back to bite you," Carlyle said. The Ducks did, however, limit Detroit to one shot in the first 10 minutes of the game and outshot the home team 10-5 in the period. Anaheim had another man advantage early in the second, but only got one shot on Hasek and couldn't take advantage of him losing his stick midway through the power play. The Ducks controlled play often over the first two periods, outshooting Detroit 18-11, but didn't have anything show for it. Their pressure paid off early in the third period when Kunitz scored on a 4-on-4 situation. Notes: Nicklas Lidstrom and Pavel Datsyuk had assists on the first goal of the game, and Lidstrom had one on the game-winning goal. ... Ryan Getzlaf's drop pass gave him an assist on the Anaheim's goal. ... Detroit and Anaheim split the season series, both teams winning twice at home. ... Both teams lost to Edmonton last year, with the Red Wings falling to the Oilers in the first round and the Ducks in the conference finals. ... Anaheim C Todd Marchant (groin) played for the first time in the postseason. ... The Red Wings were without key defensemen Mathieu Schneider (broken wrist) and Niklas Kronwall (back) ... Anaheim has just six players on its roster from the Babcock-led team in 2003. ... Chris Pronger is facing the Red Wings for the sixth time in the playoffs and one-fourth of his 120 postseason games have been against them. ... Kunitz went to college in Michigan, playing four seasons at Ferris State. ... Since 2003, Babcock has won an NHL-high 26 playoff games. AP-CS-05-11-07 2250EDT