Just one play earlier, Dolphins head coach Joe Philbin aimed to ice Folk, but instead his timeout stopped play and negated a blocked field goal by his special teams unit.
Rex Ryan and company were fortunate to come out on top and they know it.
"It looked bleak there for a while," admitted Jets head coach Rex Ryan. "We just kept fighting. We have that mentality that good things are headed our way. And we just kept believing and kept fighting."
After New York's drive stalled on their first offensive possession of the extra session, the Dolphins marched down to the Jets 30-yard line and set up for a 47-yard game-winning field goal. Miami's placekicker Dan Carpenter, who missed a 48-yard attempt early in the fourth-quarter, sent his overtime boot wide and outside the left upright, giving the Jets second-life. Mark Sanchez would capitalize on his second chance on the ensuing drive as he found wide receiver Santonio Holmes for 38-yards down the left sideline to set up Folk's walk-off kick.
Mark Sanchez struggled to find his way on Sunday
Ironically, it was Holmes who stormed off to the bench during last year's regular season finale in Miami, following a spat in the huddle with offensive lineman Brandon Moore.
"I was so proud of him," said Sanchez of Holmes' bounce back performance on Sunday. "He came back into an environment that brought back so many bad memories and for him to fight it off, (and) to make some unbelievable catches was huge."
Sanchez struggled mightily through three-quarters of play, but led Gang Green on an eight play-38 yard drive capped by a seven-yard touchdown connection with wideout Jeremy Kerley, putting the Jets ahead 20-17 with 3:01 remaining in the contest.
Miami's rookie signal-caller Ryan Tannenhill would answer back as he engineered a 12 play, 48-yard drive with Carpenter converting a 41-yard field goal attempt to send the game into overtime.
It was far from Sanchez's finest performance as he completed just 21 of 45 pass attempts for 306 yards two interceptions and one touchdown. The Jets survived a rollercoaster outing, yet found a way to outlast Miami in a game that eclipsed four hours in duration. Wildcat quarterback Tim Tebow carried the ball just two times for no yards.
Jets All-Pro cornerback Darrelle Revis left with a non-contact injury in the third-quarter after he appeared to tweak his knee and was ruled out for the remainder of the game. Miami running back Reggie Bush left the field 23 seconds before halftime after suffering left knee injury. He did not return.