Both of Holmstrom's goals came in the second period as the Red Wings took a 3-1 advantage into the final stanza.
It was Detroit's third straight win and its seventh in 10 games to open the season. Zetterberg, who assisted on Holmstrom's second goal, has a point in every game this year. He has scored seven times with 11 assists.
Dominik Hasek was called on to make only 13 saves for the Red Wings. Vancouver got off just four shots in the third period.
Vancouver lost for the fourth time in five games as Roberto Luongo was peppered with 39 shots.