Ivory, who was traded to the Jets in the off-season after three years with the Saints, carried the ball 18 times for New York (5-4), which rebounded from a 49-9 loss to Cincinnati last week.
Nick Folk kicked four field goals, improving to 23-of-23 on the season.
Geno Smith (8-of-9 passing for 115 yards) threw for a touchdown and ran for another for the Jets.
Drew Brees went 30-of-51 through the air for 382 yards with a pair of touchdown tosses to Jimmy Graham but was picked off twice for the Saints (6-2), who lost running back Darren Sproles to a concussion early in the game.
Graham finished with nine catches for 116 yards.
Swim Week Miami Beach 2014 [PHOTOS]