Zetterberg's second goal 1:20 into the third period, a wrist shot taken while cruising down the slot, blunted a Pittsburgh comeback try and re-established a two-goal cushion for the Red Wings at 3-1.
Valtteri Filppula got Detroit's other goal and added a helper while Jimmy Howard made 26 saves in the win, which gave the Wings 85 points for the season and boosted them four points ahead of Calgary for the eighth and final playoff spot in the Western Conference.
Pascal Dupuis got the lone goal for the Penguins, who have lost three of their last four games while hanging on to a two-point lead over New Jersey for first place in the Atlantic Division.
Howard and Penguins star Sidney Crosby fought each other along the boards behind the Detroit net as time expired.
Notable deaths of 2014 [PHOTOS]