Connor Barth made four field goals and Quincy 20.
Arrelious Benn and Preston Parker each had a TD catch for the victors.
Drew Brees connected on 29-of-45 passes for 383 yards, one touchdown and three interceptions for the Saints (4-2), who had a four-game winning streak snapped.
Jimmy Graham became the second tight end in NFL history to have four straight games with 100-plus yards receiving. He had seven catches for 124 yards. Former Kansas City Chief and current Atlanta Falcon Tony Gonzalez accomplished the feat in four consecutive games in 2000.
Marques Colston caught seven passes for 118 yards and a touchdown for the Saints, who played most of the game with assistant coach/linebackers coach Joe Vitt calling the plays.
New Orleans head coach Sean Payton suffered a torn MCL and a broken tibia following a collision along the sideline early in the first quarter.
Payton was supposed to coach the second half from the booth, but was unable to because of the severity of the injury. He will have surgery Monday morning.