Patriots quarterback Jones, whose future had come under scrutiny after a dismal 1-5 start to the season, kept his composure superbly on a final drive with less than two minutes remaining before finding Mike Gesecki with a one-yard touchdown pass.
That decisive score with just 12 seconds left on the clock sealed a roller coaster win for Patriots -- the 300th regular season victory of New England coach Bill Belichick's career.
Moments earlier, it looked as if the Patriots were set to suffer an agonizing defeat after the Bills hauled themselves back from a 12-point deficit midway through the fourth quarter to lead 25-22.
The Patriots had appeared poised for a comfortable win after Jones found Kendrick Bourne for a four-yard touchdown pass that helped make it 22-10 with 7min 36sec remaining in the fourth.
But the Bills looked to have turned the game on its head with two quickfire touchdown drives to regain the lead.
Wide receiver Stefon Diggs narrowed the deficit to 22-17 after gathering a pass from quarterback Josh Allen on the slide before spinning away from the Patriots defense to scamper over for a touchdown.
A Patriots fumble on the next drive then presented Buffalo with a chance to take the lead, and Allen duly seized the opportunity after rushing over from one yard before a two-point conversion gave the Bills a three-point cushion.
Just as Patriots fans began to fear a sixth defeat of the season, Jones came up big with the drive that secured victory.
Jones finished on 272 passing yards with 25-of-30 completions and two touchdowns. Allen had 265 yards from 27-of-41 passes.
In other early games on Sunday, the Detroit Lions' credentials as potential Super Bowl contenders took a pummeling in a 38-6 beatdown by the Baltimore Ravens.
Ravens quarterback Lamar Jackson turned in a dazzling display to outshine Lions counterpart Jared Goff, throwing for three touchdowns and rushing for another while piling up 357 passing yards in a comfortable win that saw Baltimore improve to 5-2 at the top of the AFC North division.
Detroit fell to 5-2 but still lead the NFC North.
In Indianapolis, Kareem Hunt rushed over for a close-range touchdown on fourth down with just 15 seconds remaining to give the Cleveland Browns a thrilling 39-38 victory over the Colts.
Browns running back Hunt barged his way into the end zone to seal a crucial win for Cleveland, which saw quarterback Deshaun Watson leave the game early on with an injury.
Elsewhere, the Chicago Bears claimed only their second win of the season with a 30-12 defeat of the Las Vegas Raiders as backup quarterback Tyson Bagent throwing for 162 yards and one touchdown.
D’Onta Foreman rushed for two touchdowns and 89 yards from 16 carries to guide the Bears to victory.
