Woodson scooped up a fumble by Washington wide receiver Santana Moss and the fourth touchdown of his career erased a 14-10 deficit with 2:05 left in the third quarter.
Green Bay quarterback Brett Favre completed 19 of 37 passes for 188 yards, but two picks made him the NFL's all-time leader in passes intercepted with 278, moving him past George Blanda.
DeShawn Wynn rushed for a touchdown on 13 attempts for just 37 yards, and Donald Lee made three receptions for 75 yards as the Packers improved to 5-1 for the season.
Washington quarterback Jason Campbell threw for one touchdown on 21-of-37 passing for 217 yards.
Celebrity Families of 2014 [PHOTOS]