Lee Stempniak scored his first goal as a member of the Penguins and added two helpers, Chris Kunitz also recorded a multi-point game with a goal and an assist, and Brandon Sutter tacked on a late shorthanded tally.
Jeff Zatkoff made 32 saves for Pittsburgh, which bounced back from a weekend home-and-home sweep at the hands of the Philadelphia Flyers.
Kari Lehtonen, playing in his first game since suffering a concussion against the Wild on Mar. 8, gave up all five goals on 32 shots in his return.
Dallas has dropped three straight and still sits two points behind the Phoenix Coyotes for the second wild card position in the Western Conference.