Sharper picked off a Mark Sanchez pass and raced for a touchdown and Remi Ayodele got the other score, on a fumble by Sanchez, within a 6-minute span in the second quarter, giving the Saints a 17-0 lead.
New Orleans (4-0) also had a 1-yard touchdown run by Pierre Thomas and a 34-yard field goal by John Carney.
Drew Brees completed 20-of-32 passes for 190 yards for the Saints.
Sanchez, 14-of-27 for 138 yards, had four turnovers, three of them interceptions, and was sacked four times
The Jets (3-1) scored on a 15-yard run by Thomas Jones and Jay Feely's 38-yard field goal.