Minnesota secured the victory with a goal-line stand in the final minute to win for the second time this season.
Vikings quarterback Christian Ponder threw two touchdown passes before exiting with an injured left shoulder late in the third period, leaving it up to Matt Cassel to finish off the go-ahead touchdown drive.
Minnesota improved to 2-7 while the Redskins fell to 3-6. Washington failed in its bid to win back-to-back games for the first time this season.
Washington built a 27-14 lead midway through the third period, but the Vikings made it a one-score game when Ponder hit John Carlson with a 28-yard scoring pass with 4:32 left in the quarter.
Ponder again led the Vikings deep into Washington territory and he came close to scoring when he tried to stretch the ball over the goal line at the end of a 15-yard run. It was on that play that Ponder was injured and Cassel came in to hand the ball off to Peterson for the go-ahead touchdown.
Field goals of 30 and 40 yards increased Minnesota's lead to seven points in the fourth quarter and the Vikings then survived a late drive engineered by Washington quarterback Robert Griffin III.
Griffin marched the Redskins from their own 20-yard line to a first down on the Minnesota 8 and Roy Helu then ran the ball to the Vikings' 4.
From there, however, Griffin threw three straight incompletions to leave Minnesota with the win. Griffin was 24-of-37 for 281 yards and three touchdowns, but still came up second best. Washington's Alfred Morris gained 139 yards on 26 carries.