Young engineered the 80-yard drive after Eli Manning had forged a 10-10 tie with a 24-yard scoring strike to Victor Cruz earlier in the final frame.
Young, substituting for the injured Michael Vick, found Riley Cooper down the middle with an 8-yard touchdown pass with 2:45 remaining and Philadelphia (4-6) sealed the win when Manning lost a fumble after a Jason Babin sack.
Young overcame three interceptions, finishing 23-of-36 for 258 yards with two touchdowns.
LeSean McCoy carried the ball 23 times for 113 yards for the victors.
Manning went 18-of-35 through the air for 264 yards, a touchdown and an interception for the Giants (6-4), who fell into a tie with Dallas atop the NFC East.