Both defenses were on top early in the game, but the Cardinals drew first blood when Carson Palmer lifted the ball down the middle of the field for Michael Floyd, and he made an impressive leaping catch for a 20-yard touchdown.
Washington hit back almost immediately with a simple pass play over the middle of the field as Kirk Cousins fired to DeSean Jackson, and the receiver found a crease in the defense and ran all the way for the 64-yard score.
Another big reception from Jackson put the Redskins on the move again into the redzone, but they failed to punch the ball in for seven-point score and were forced to settle for a 28-yard field goal from Kai Forbath.
The Cardinals regained the lead at the end of the second quarter when Palmer hit Larry Fitzgerald on a slant route over the left side of the field, and he shrugged off a defender to run in for the touchdown.
Forbath added another field goal just before the whistle to reduce his side's deficit to a single point.
In the second half, the Cardinals put some distance between themselves and the Redskins when Chandler Catanzaro fired a field goal between the posts from 33 yards.
Catanzaro added another field goal early in the fourth quarter and a fumble by Andre Roberts allowed the kicker to convert again as his side's struggles in the red zone in the second half continued.
Despite throwing two interceptions in the fourth quarter Cousins brought the Redskins back into the game with two minutes remaining as he found Pierre Garcon in the endzone for a five-yard touchdown.
However, with the chance to tie the game in the dying seconds, Cousins threw an interception straight into the hands of Rashad Johnson, who returned the ball for a touchdown to seal Arizona's victory.