Campbell drove the Bears 58 yards in 11 plays to the winning touchdown.
Chicago ultimately secured the exhibition victory when Isiah Frey intercepted a pass in the end zone by New York's David Carr from the Bears' 13 with 1:13 to play.
Bears starter Jay Cutler went 9-of-21 for 96 yards for a touchdown. Campbell then completed 12-of-19 for 101 yards.
Brandon Marshall caught five passes for 51 yards and a touchdown as Chicago won for the second time in three exhibition games.
New York's Eli Manning completed 17-of-21 for 148 yards.
Giants cornerback Prince Amukamara left the game on a cart in the first quarter after suffering a sprained ankle. X-rays were negative but the New York Daily News reported Amukamara suffered a high right-ankle sprain that could keep him out as long as six weeks, maybe more.
New York fell to 1-2 in the pre-season.