Both teams emerged with a 4-2 record after an entertaining contest that was tied on three occasions and in which the lead changed hands twice.
Buffalo put itself in position to take the lead by marching to the Giants' 27, but Fitzpatrick's deep pass on first down was intercepted by Corey Webster at the New York 4-yard line.
That touched off a nine-play drive that led to Tynes' game-winning field goal.
Buffalo failed to pick up a first down on its next possession and turned the ball over at its own 25.
Ahmad Bradshaw scored all three of New York's touchdowns, each of them coming on a 1-yard run. He gained 104 yards on 26 carries. Eli Manning completed 21-of-32 passes for 292 yards.
Fitzpatrick went 21-of-30 for 244 yards, but was intercepted twice. Webster recorded both interceptions.