Backup Chad Henne added 28 yards and a score, while Jordan Palmer chipped in 110 yards and a go-ahead TD pass to Matt Veldman late in the fourth quarter.
Mike Thomas led Jacksonville with four receptions for 89 yards.
The Giants' Eli Manning started the game, going 4-of-8 passing for 60 yards.
Back-up David Carr, meanwhile, tossed two touchdowns and picked up 48 yards through the air.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys