Denarius Moore and Michael Bush scored touchdowns 42 seconds apart in the second half for Oakland (2-1), which has won 10 of the past 13 home games against the Jets.
"I just shows what our team can do," McFadden said. "If we come out here week and week out we can play with anybody in the league."
Raiders quarterback Jason Campbell completed 18-of-27 passes for 156 yards.
Mark Sanchez threw for 369 yards, two touchdowns -- he added another score on the ground -- and one interception on 27-of-43 attempts for New York (2-1).
Trailing 17-7 in the second quarter, McFadden made it a one-possession game with a 70-yard dash to the end zone. Sebastian Janikowski drew Oakland even by drilling a 54-yard field goal as the first half ended.
The Jets were denied on 4th-and-2 at the Oakland 37 late in the third quarter. On the fourth play of the ensuing drive, Moore took a reverse and ran 23 yards for the go-ahead score with 40 seconds remaining.
New York muffed the kickoff and the Raiders recovered deep in Jets' territory. Two seconds into the fourth quarter, Bush powered his way up the middle from a yard out to put Oakland up 31-17.
Later in the frame, Sanchez hit Plaxico Burress for a 16-yard touchdown, capping a 10-play drive that originated from the New York seven.
Janikowski provided some insurance by converting a 49-yarder with 2:37 to play.
Sanchez then led the Jets down the field and scrambled for what looked like a two-yard touchdown on 4th-and-goal. However, a video review determined Sanchez was short of the end zone.
The game's opening drive culminated in a two-yard TD run by McFadden, but New York countered later in the first quarter on a one-yard run by Sanchez.
"We had momentum going in our favor, but let them hang around," Sanchez said. "This is a good enough team. They're starting to get good at it with a new head coach."
McFadden carried 19 times for 171 yards...Tomlinson, who caught five passes for 116 yards, became the third player in NFL history to record 160 touchdowns, joining Hall of Famers Jerry Rice (208) and Emmitt Smith (175).