Lynch's scoring run with 7:08 left in the game gave the Seahawks their first lead and Steven Hauschka added the second of his two field goals 1 1/2 minutes later following a Robert Griffin III fumble to seal the victory.
Lynch finished with 132 yards on 20 carries and Russell Wilson accounted for 254 total yards with a touchdown pass as Seattle overcame a 14-0 first-quarter deficit to advance to next week's divisional round.
There they will next play at NFC top seed Atlanta.
Wilson went 15-of-26 through the air for 187 yards and carried the ball eight times for 67 yards as the Seahawks broke an eight-game post-season road losing streak.
Griffin completed 10-of-19 passes for 84 yards, two TDs, an interception and a lost fumble for the Redskins, re-injuring his troublesome right knee in the fourth quarter.
Logan Paulsen and Evan Royster each caught a scoring pass for the losers.