Zetterberg collected a deflection in the left circle and put a slapshot past Roberto Luongo, vaulting the Red Wings back into first place in the Western Conference. Detroit had given up leadership of the conference to Dallas Tuesday.
Zetterberg's first goal tied it at 3-3 1:54 into the third period. Jeff Tambellini put Vancouver in front midway through the stanza and Nicklas Lidstrom again tied it on the power play with 3:54 to go in regulation.
Detroit, which dropped three of its previous four games, lost forward Pavel Datsyuk to an upper-body injury in the opening period.
Jimmy Howard got the win by making 35 saves.
Daniel and Henrik Sedin had a goal and an assist each for Vancouver, which had won four in a row. Luongo stopped 40 shots.