The Cowboys went into the clash at the AT&T Stadium with a six-game winning streak to maintain, as they looked to continue their push for the playoffs.
However, their bid to extend that streak suffered an early hitch when Kai Forbath kicked a 44-yard field goal after five minutes in what proved a cagey opening quarter in Texas.
A sack of Romo just before the break prevented the Cowboys from extending their lead as Ryan Kerrigan brought the quarterback down for a 12-yard loss.
In the second half, the Redskins responded and came out with an excellent drive led by Colt McCoy, which culminated in a touchdown as Alfred Morris ran into the endzone for a five-yard score.
The turning point in the game occurred when Romo went down with a back injury after he was sacked by Keenan Robinson and replaced by Brandon Weeden. However, Weeden soon led his side to level the scores as Dan Bailey kicked over from 21 yards.
Washington wrestled back the initiative in the match when McCoy reeled off another impressive drive as he hit DeSean Jackson on a deep pass downfield. The quarterback ran in for the touchdown himself with a seven-yard run.
Weeden rallied the Cowboys with Romo still on the sidelines, and again he tied the game with a 25-yard strike to tight end Jason Witten late in the fourth quarter.
Neither side could score again in regulation, as Romo returned to the game and nearly cost his team the match with a fumble on his own five-yard line, but Joseph Randle gathered the ball.
In overtime, the Redskins once again moved seamlessly downfield and Forbath fired them ahead with a 40-year field goal.
Needing a touchdown to win the game or a field goal to keep the match going, Romo failed to convert on fourth down as his side fell to their second defeat of the season.