The Jets got off to a great start defensively when they put pressure on Tampa Bay quarterback Josh Freeman, as he fumbled the ball and it bounced out of the endzone leading to a two-point safety for the home side.
Freeman responded to this with a solid drive down field and gave his side the lead when he and receiver Mike Williams combined for a 17-yard touchdown, while Ryan Lindell added the extra point.
The Jets got their offense going after a turnover and Folk was able to get three points on a 43-yard field goal.
Tampa took full advantage as Doug Martin powered over to score the touchdown to give his side a 14-5 lead.
Smith rallied his offense and drove down the field going five-for-five before firing a strike to Kellen Winslow to make the score 14-12.
The teams played out a scoreless third quarter as both quarterbacks struggled to find their rhythm, while the defenses began to dominate the game.
Smith finally put a drive together in the fourth quarter allowing Folk an opportunity to give the Jets the lead with a 30-yard field goal, which he duly knocked through the posts.
However, late in the game Tampa Bay retook the lead with a field goal of their own, thanks to a 37-yard Lindell effort.
Just when the Buccaneers thought that they had secured the game, Lavonte David was penalised for a personal foul on Smith when he pushed him out of bounds, which put the Jets into field goal range.
Folk delivered with a 48-yard field goal to hand the Jets a 18-17 victory at MetLife Stadium.