Evgeni Malkin scored the only goal needed for the Penguins, who have won three straight.
Henrik Lundqvist had 21 saves for the Rangers, who have lost four straight and six of their last seven games.
The Penguins scored the game's only goal 44 seconds into the second period. Ryan Whitney controlled the puck in the left corner and sent a pass across the crease to Malkin, who redirected the disc over the goal line.
Seconds later, Pittsburgh had a chance to increase its lead as Jordan Staal was hooked down on a breakaway and awarded a penalty shot. Lundqvist made a stick save on Staal's shot to keep it a one-goal game.