The Patriots' defence intercepted Jones three times and scored a fourth-quarter touchdown on a return of a fumble recovery.
The win leaves the Pats 6-0 and on top of the AFC East, while the loss leaves the Giants on 2-4 and second from the bottom in the NFC East.
The final score was a little unfair to the visitors. The Giants were tied 14-14 in the second quarter were within seven points of the Patriots in the final quarter.
The Giants also scored a second-quarter touchdown on a return of a fumble by Patriots quarterback Tom Brady on a sack.
But in the fourth quarter, Brady scored his second rushing touchdown of the game and the Patriots' unbeaten start to the season continued.