Goaltender Dominik Hasek made 29 saves for his 14th career playoff shutout as the Wings took a 2-1 lead in the series. Holmstrom scored on a first-period power play, then made it 4-0 on a wrap around early in the second.
He left the game at 11:40 of the second with blood dripping from his forehead after being smashed into the boards by Duck defenceman Chris Pronger and forward Rob Niedermayer.
The hit knocked Holmstrom's helmet off and the left-winger crumpled to the ice were he lay flat for several minutes. The Detroit training staff rushed onto the ice and helped him to the dressing room.
Niedermayer was given a five-minute boarding penalty and a game misconduct on the play.
Holmstrom returned early in the third after receiving stitches for two cuts and assisted on Valtteri Filppula's goal.
Johan Franzen and Todd Bertuzzi scored the other Detroit goals. Henrik Zetterberg and Nicklas Lidstrom had two assists each.
Game 4 in the best-of-seven series will be played Thursday at the Honda Center.
A sellout crowd of 17,358 was sent home disappointed. The Ducks tested Hasek early, forcing him to make saves on Andy McDonald and Pronger, but after that Detroit took over the play.
The Ducks didn't help their cause by taking a string of penalties and losing their cool as the game progressed.
After putting the Ducks in a hole with two goals in the first period, Detroit sealed the deal by scoring twice in 17 seconds in the second. The Wings outshot Anaheim 13-2 in the period.
Bertuzzi made it 3-0 at 3:17 when Dan Cleary's pass bounced off his stick, hit Ducks goaltender J.S. Giguere and went into the net. That ended Giguere's night as he was replaced by backup Ilya Bryzgalov.
Bryzgalov didn't fare much better, allowing Holmstrom's second goal on the first shot he faced.
Franzen made it 1-0 midway through the first period when he directed a cross-ice pass from Mikael Samuelsson past Giguere. Defenceman Scott Niedermayer appeared to have a chance to breakup the play but the puck bounced over his stick, giving Detroit its first even-strength goal of the series.
Holmstrom made it 2-0 with just 43 seconds left in the period with Pronger watching from the penalty box after being sent off for hooking Bertuzzi. Holmstrom scored after taking a pass from Zetterberg and beating Giguere with a hard shot.
It was the first power-play goal the Ducks had allowed at home during the playoffs.
Anaheim played without forward Chris Kunitz who is gone for the layoffs with a broken bone in his right hand.
Detroit's Tomas Kopecky, who was inserted into the lineup for Kyle Calder, had a tough first period in his first Stanley Cup playoff game. He was called for two penalties, hooking and delay of game after shooting the puck over the glass.
Kopecky, Detroit's second-round pick in the 2000 draft, had been out since suffering a broken clavicle at Chicago on Dec. 14.
Notes: Celebrities at the game included actors John Cusack and Cuba Gooding Jr., rocker Kid Rock and Olympic silver medallist figure skater Sasha Cohen. ...The previous three times the Ducks and Wings met in the playoffs, the series all ended in sweeps. Detroit won in 1999 and 1997 while Anaheim took the 2003 series. ...When Teemu Selanne played his first NHL season with the Winnipeg Jets in 1992-93 Ducks coach Randy Carlyle was in the final year as a player. ...Scott Niedermayer's 12 career overtime goals is tops all-time among NHL defencemen.