Rodgers completed 34-of-42 passes with four touchdowns, tying the Packers' mark for most passing yards in a single game set in 2011 by Matt Flynn.
James Jones hauled down 11 Rodgers passes for 178 yards while James Starks led the Packers' ground game, rambling for 132 rushing yards and a touchdown on 20 attempts.
Green Bay (1-1) rolled up 580 total yards of offense en route to its first win of the season following a 34-28 loss to San Francisco.
The Redskins (0-2), meanwhile, remained mired in an early-season slump after falling behind 31-0.
Robert Griffin III made good on 26-of-40 passes for 320 yards, three touchdowns with an interception while Pierre Garcon made eight catches for 143 yards and a score in the loss.