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Pierre Garcon restored the Washington lead and Forbath added a field goal as the Redskins appeared to be surging ahead, but Jordan Matthews scored his debut NFL touchdown to get the Eagles back into the game.
Foles pushed for another score before the break, and managed to connect with Matthews again late in the second quarter to put Philadelphia ahead by a single point.
Cody Parkey picked up a couple of field goals in the third quarter to extend the home side's lead, but an 81-yard touchdown pass from Cousins to DeSean Jackson got the sides back level again heading into the final 15 minutes.
The late hit resulted in players from both teams becoming involved in a mass brawl on the field, eventually resulting in Jason Peters being ejected from the game for retaliating at Baker, while Baker was also removed from the game for the hit.
Foles shook off the hit to continue in the game, leading a lengthy drive before throwing a 27-yard pass to Jeremy Maclin to put Philadelphia back in front.
Washington responded quickly, with Roy Helu sprinting for a big gain down the sideline before powering over for a one-yard touchdown off the next play, leaving the Redskins just three points down, with over four minutes still on the gameclock.
However, the Eagles managed the clock to ensure that they kept the ball for the final minutes of the game, maintaining their unbeaten start to the season, while the Redskins slip to 1-2.