Hiller made 45 saves in his second sharp outing of the series and survived a furious Detroit rally in the third period that included the potential tying goal being waved off by the referee with 1:09 to play.
Anaheim took a 1-0 lead on Selanne's breakaway goal at 12:49 of the first period. The Ducks extended the lead to 2-0 on a power play at 8:16 of the first when Niedermayer somehow knocked the puck into the net amid a scrum in front of Osgood.
The Red Wings did not get one past Hiller until 5:40 remained in the second period when Zetterberg punched in a rebound on a Detroit power play.
Osgood was pulled in favor of a sixth skater as the game drew to a close. Marion Hosa pushed in a puck that had gotten loose in the crease but referee Brad Watson apparently lost sight of the puck and blew his whistle to stop play before it crossed the line.