Detroit put the game on Darren Helm's first playoff goal with 3:08 remaining in regulation and Zetterberg's empty-net goal wrapped up the scoring.
After a scoreless first period, the Red Wings took a 2-0 lead early in the second period. Johan Franzen flipped in a wrist shot at 3:23 and was followed at 4:02 Jiri Hudler, who knocked in a follow-up to Zetterberg's shot on a charge to the crease.
Ryan Whitney scored the lone Ducks goal at 15:37 of the period on a power play.
Game 6 is set for Tuesday in Anaheim.