Janikowski hit the long kick with 2:30 remaining in the extra session.
JaMarcus Russell was 17-of-30 passing for 203 yards and a touchdown for the Raiders (2-4).
Javon Walker caught five passes for 75 yards and a touchdown for Oakland, which had lost its previous three games.
Jets quarterback Brett Favre directed a last-minute scoring drive to send the game into overtime.
Favre finished 21-of-38 for 197 yards and was intercepted twice.
Thomas Jones rushed 24 times for 159 yards for the Jets (3-3).