Russell Wilson outdueled Robert Griffin III in the celebrated clash of outstanding rookie quarterbacks, but the dynamic Redskins' signal caller was hampered by a knee injury and forced to leave the game in the fourth quarter.
After a pair of four-yard touchdown passes by Griffin on Washington's first two possessions, Seattle's defence shut them down and Wilson brought the Seahawks back to 14-13 by halftime and added 11 points in the fourth quarter for the victory.
Wilson joined Seattle as the 12th pick in the third round of the draft from the University of Wisconsin - the 75th most sought-after recruit - after being written off by some teams as not tall enough at a shade under 5-foot-11 (1.80 metre).
"People always ask me if I have a chip on my shoulder because I was a third-round draft pick. If I was first pick overall or picked in the third round, where I was, I'm blessed to be a Seattle Seahawk," Wilson said afterwards.
It was the first road playoff victory for the Seahawks in 30 years and propelled them to a divisional round clash against the NFC South champion Atlanta Falcons next weekend.
Washington moved through a Seattle defence that led the NFL in fewest points allowed in the regular season with ease at the start of the game as Griffin engineered scoring drives of 80 yards and 54 yards culminating in short touchdown passes to Evan Royster and Logan Paulsen.
The Seahawks took charge in the second quarter, dominating play with a pair of field goals and an eight-play, 73-yard touchdown drive capped by a four-yard TD pass from Wilson to fullback Michael Robinson.
Seattle continued to dominate after intermission, but squandered points when running back Marshawn Lynch fumbled at the one-yard line on an attempted scoring plunge in the third quarter.
Washington clung to their one-point advantage, despite failing to mount any offensive threats, with Griffin visibly limping and having trouble avoiding the pass rush.
A brilliant, 27-yard touchdown run by Lynch finally put the Seahawks ahead and tight end Zach Miller caught a Wilson pass in the end zone for a two-point conversion to make it 21-14.
Facing a second-and-22 in the shadow of the Washington end zone, Griffin could not handle a poor snap and Seattle recovered on the five-yard line and limped off the field with around six mounts to go.
"I didn't get hit, I just planted it wrong," Griffin explained after the match.
"My knee kind of buckled on me and scared me a little bit, so I want to the sideline and got a tape job done on the knee.
Griffin, 22, became the first quarterback born in the 1990s to start an NFL playoff game.
"We know the future is very bright. I also know what I need to work on in the off-season. Part of that is just getting healthy. The sky's the limit for this team with the talent we have," Griffin said.
Seattle could not punch it in, but settled for a 22-yard field goal that put the game out of reach at 24-14.