Zetterberg, who also notched an assist, banked a puck into the net off Minnesota goalie Niklas Backstrom just 4:38 into the game. Cleary followed that up with a shot from a sharp angle that eluded Backstrom 4 minutes later.
Niklas Kronwall assisted on Zetterberg's score and on the Wings' third goal, in which Kris Draper made it 3-0 early in the second.
Tomas Holmstrom also scored and Jimmy Howard stopped 16-of-17 shots for Detroit.
Brent Burns tallied for Minnesota and Backstrom ended up stopping 23-of-27 shots.