The scores came after the Jets took an early 3-0 lead after driving 83 yards on their first possession.
That came after Miami went three-and-out on its first drive. But the next three times the Dolphins had the ball, they marched 71, 79 and 84 yards to take their commanding lead.
Williams was the driving force on offense all day, as he rushed 30 times for 130 yards and also caught four passes for 38 more yards.
Things got a little dicey after Fiedler fumbled on the first play of the fourth quarter and the Jets scored six plays later on Vinny Testaverde's 33-yard touchdown pass to Santana Moss.
But the Jets never drove beyond the Dolphins 30-yard line the rest of the game, as the Dolphins evened their record at 1-1, with the resurgent Buffalo Bills coming to Pro Player Stadium next Sunday night.