Washington trailed 3-0 after the first period but shut the door after that, chipping away with goals from Mike Ribeiro and Tomas Kundratek in the second period.
Wojtek Wolski connected for the tying score late in regulation and Fehr got the game-winner on a play in which he shook off a pair defenders on a rush down the middle and flipped a shot past Tuukka Rask.
Braden Holtby ended with 30 saves as the Caps won for the fourth time in five outings.
Brad Marchand, Dougie Hamilton and Zdeno Chara found the net for the Bruins and Rask finished with 20 saves in the loss.
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