Brian Westbrook rushed for 81 yards and caught nine passes for 63 yards in the Eagles' win.
Reggie Brown caught the only touchdown of the game for Philadelphia (6-8).
Romo finished 13-for-36 passing and saw his streak of 17 consecutive games with a touchdown pass come to an end.
The loss leaves Dallas (12-2) in a tie for the top spot in the NFC with Green Bay.
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