Smith's 17-yard scoring run with 3:26 remaining sealed the victory for the Jets (7-8), who won for just the second time in six games.
The New York quarterback completed 20-of-36 passes for 214 yards, including two scoring throws to David Nelson.
Christopher Ivory ran for 109 yards on 20 carries.
The Browns (4-11) dropped a sixth straight despite 97 receiving yards on six catches by Josh Gordon.
Edwin Baker picked up 64 rushing yards on 17 carries for Cleveland.