Washington cornerback Bashaud Breeland picked off Sanchez's pass with one minute and 36 seconds remaining on Saturday and the Redskins capitalised, driving 50 yards before Kai Forbath slotted his second field goal of the game to end the home side's six-game losing streak on Saturday.
The result just about ended the Eagles' hopes of making the NFL play-offs as well, with Philadelphia suffering their third consecutive defeat to remain a win behind the Dallas Cowboys at the top of the National Football Conference's (NFC) East division.
A week ago, the Eagles still led the NFC East but unless the Cowboys lose to the Indianapolis Colts on Sunday, Philadelphia will be eliminated from the play-offs race ahead of next week's final round of the regular season.
Errors again cost Philadelphia with Sanchez turning the ball over twice - one fumble lost and Breeland's decisive interception - for 13 in seven matches, while the Eagles lead the NFL with 36 turnovers for the season.
The visitors led 14-10 at half-time after Sanchez picked out Riley Cooper in the end zone midway through the second quarter but a dominant third quarter set up the Redskins' win.
On their first drive, fullback Darrel Young finished off for the hosts with a one-yard run for a TD.
And, after Philadelphia kicker Cody Parker missed a field goal, Young scored on the Washington's second drive of the term to give the Redskins a 10-point lead with a quarter to play.
While the Eagles dragged themselves level, Washington would prevail in the end when Forbath made it five successful kicks from as many attempts, converting the match-winning goal from 26 yards.
The victory took Washington to a 4-11 win-loss record this season as the bottom of the NFC East, while Philadelphia (9-6) trail the Cowboys (10-4).
In the other match, a fumble by San Francisco 49ers wide receiver Quinton Patton allowed the San Diego Chargers to come from behind and win 38-35 in overtime.
The 49ers had led by as much as 21 points early in the second quarter at home, while a 90-yard rushing touchdown by quarterback Colin Kaepernick with 2:26 left in the third term saw the hosts up 35-21.
But with Chargers QB Philip Rivers throwing two TDs in the final term and Nick Novak slotting both conversions, San Diego forced overtime at Levi's Stadium.
In the extra period, Kaepernick handed off to Patton on just his second play and while the wide receiver charged 20 yards to earn a first down, he lost the ball in a tackle by Eric Weddle and the Chargers gained possession.
Rivers led the visitors to within 40 yards of goal before Novak stepped up to clinch victory for San Diego.