New York got two points on a safety when Tom Brady was called for intentional grounding on New England's first play from scrimmage.
The Giants ran 19 of the game's first 20 plays from scrimmage, capped by Manning's short pass to Cruz behind two defenders with 3:24 left in the quarter.
Brady's pass, under pressure, was thrown 45 yards downfield from the front of the end zone with no receiver in the vicinity. The Patriots were driving as the quarter ended.
The game is a rematch of the 2008 Super Bowl. The Giants won that game, 17-14, on Plaxico Burress' 13-yard touchdown catch with 35 seconds remaining.
It's also a rematch of a Week 9 game this season. Manning also threw a touchdown pass in the final minute of that one to give the Giants a 24-20 win over the Patriots.