Letang's tally 7 minutes into the second period broke a 2-2 tie and Kunitz iced the contest with back-to-back goals 6 1/2 minutes apart for the Penguins, who logged their fourth win in five games and second in two days.
Tomas Vokoun stopped 21-of-24 shots for the Penguins.
Mike Ribeiro recorded a goal and assist and Braden Holtby was torched for all six goals on 26 shots as the Capitals continued their sluggish start, falling to 2-6-1 on the season.
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