Washington has lost four games in a row, the last two under new coach Dale Hunter. The Capitals have dropped eight out of 10 overall.
Kunitz scored his ninth goal of the season 2:36 into the final period, boosting the Penguins to just their third win over Washington in their last 14 meetings.
The Penguins have gone 4-2 since Sidney Crosby returned from his almost yearlong absence. Crosby recorded 11 points in his first five games back, but did not have one Thursday while taking three shots.
Tomas Vokoun made 33 saves for the Capitals. Washington had only two shots during the third period.