Jernigan scored on a 24-yard pass from Eli Manning in the second quarter and added a 49-yard scoring run in the third, finishing with 90 yards on six catches and 57 rushing yards on a pair of carries.
Manning made good on 10-of-24 passes for 152 yards with an interception before leaving late in the first half with a sprained left ankle for the Giants (7-9), who forced four Redskins turnovers on defense.
New York won for a seventh time in 10 games, but couldn't overcome a an 0-6 start to the season.
Washington (3-13), meanwhile, dropped an eighth straight to end the season amid reports head Coach Mike Shanahan would be fired.
Celebrity Families of 2014 [PHOTOS]