Ponder was hurt early in the second half, suffering a concussion on a combined sack by London Fletcher and Adam Carriker.
But Webb stepped into the breach, passing for a pair of touchdowns and running for another for the Vikings (3-12), who snapped a six-game losing streak.
Also going down to an injury was star Vikings running back Adrian Peterson, who left after sustaining a helmet-to-knee hit from Redskins safety DeJon Gomes at the start of the second half.
Toby Gerhart, however, came in and rushed for 109 yards on 11 carries for Minnesota.
The Redskins (5-10) were led by Rex Grossman with 284 yards, two touchdowns and one interception on 26-of-41 passing efficiency.
Evan Royster rolled up 132 rushing yards on 19 carries and Graham Gano kicked four field goals for Washington.