Fehr broke a 1-1 second-period tie with his first goal when Pittsburgh goalie Marc-Andre Fleury lost control of the puck behind his own net, Marcus Johansson recovered it and fired a pass to the Capitals' right winger, who put it past a scrambling Fleury.
Fehr gave Washington a 3-1 advantage 12 minutes into the final frame when he broke in alone on Fleury after receiving a pass form Jason Chimera and fired a wrist shot into the net, ensuring the Caps' win in the fourth annual NHL Winter Classic.
A light but steady rain and warm temperatures made for puddles of water on the ice. The game had been pushed back from a 1 p.m. to an 8 p.m. start to allow the ice to become firmer.
Mike Knuble also scored and Semyon Varlamov made 32 saves for the Capitals, who stayed even with Tampa Bay atop the Southeast Division with the win.
Evgeni Malkin got the only goal for the Penguins. Fleury stopped 29-of-32 shots in the loss, Pittsburgh's fourth in five games.