The Buccaneers made a bright start, adding a couple of early field goals, but Mike Evans was prevented from getting into the endzone by Jason Pierre-Paul, who was playing his first game since having his right index finger amputated.
Connor Barth added a field goal just before half time to keep Tampa Bay in contention, but the Giants soon had the ball back after the break as Doug Martin fumbled the ball, allowing Josh Brown to add another three points with the boot.
The Buccaneers fought back though, with Barth making a 53-yard kick in wet conditions, before Alterraun Verner intercepted a Manning pass intended for Beckham, but the home side could not create anything from it, forcing them to punt for the first time in the game.
Tampa Bay quickly got the ball back though, and managed to close the gap at the start of the fourth quarter as Jameis Winston scrambled to the corner, but the hosts could not tie the scores, as the two-point conversion attempt was caught out of bounds.
The Giants tried to create something on their next drive, with Beckham pulling down a 24-yard catch, but he could not hold onto another long throw from Manning, leaving Brown to kick a 53-yard field goal.
Winston continued to look for Evans as the home side sought another touchdown to keep them in the game, but the wide receiver was tackled short, while Charles Sims could not hold onto a short pass from the rookie quarterback.
The home side tried to keep the ball alive in the final seconds, needing a touchdown and a two-point conversion to force overtime, but Logan Mankins fumbled the ball following a series of lateral passes, leaving Trevin Wade to run it back for a Giants score.
The win keeps the Giants at the top of the NFC East, while the Buccaneers remain bottom in the NFC South.