Washington then scored 23 unanswered points before Philadelphia placekicker David Akers booted a 23-yard field goal with 7:18 remaining.
Washington quarterback Jason Campbell completed 16-of-29 passes for 176 yards and established a franchise record by throwing 162 passes without an interception.
Shaun Suisham kicked three field goals.
For the Eagles (2-3), Donovan McNabb went 17-for-29 for 196 yards with no touchdowns.
Westbrook was held to 33 yards on 12 carries, but caught six passes for 51 yards, and Reggie Brown made four receptions for 84 yards.
The Redskins have finished their road schedule against fellow NFC East members this season.
Rosie O'Donnell unveils nearly 50-pound weight loss
Justin Bieber crashes Drake Bell's album release party