The coach who earlier this week made the game a coach vs. quarterback matchup needed a kicker to beat Manning.
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With his main tormentor out of the way, New York (12-5) heads to New England for a third meeting next Sunday; they split during the season, but the Patriots won 45-3 at Foxborough.
The Colts (10-7) beat the Jets for the AFC title a year ago. But both defending conference champs were eliminated from the playoffs Saturday. New Orleans, which beat Indy in last February's Super Bowl, lost at Seattle.
It was a remarkable turn of emotions for the Colts, who thought they won it when Adam Vinatieri made a 50-yard field goal with 53 seconds to go.
But Antonio Cromartie returned the ensuing kickoff 47 yards and Mark Sanchez needed five plays to get the Jets into position for the winner.
"I'll tell you what, it feels awesome because this is the playoffs and we're moving on," Ryan said. "You know, he (Manning) is the best, and he almost did it to us again."
Manning certainly had his chances.
He was 18 of 26 for 225 yards and one TD, and got Vinatieri, considered the best clutch kicker in league history, in position with an eight-play, 48-yard drive in the final 2 1/2 minutes.
But he left 53 seconds on the clock for New York.
After Braylon Edwards made a leaping 18-yard catch to take New York to the Colts 14, Folk's kick went right down the middle.
Tomlinson, considered washed-up by some, carried 16 times for 82 yards and scored on two 1-yard runs.
"It's emotional, exciting and all those things at once," Tomlinson said. "We knew it was going to be a dogfight against a great team."
The Colts actually helped the Jets' winning drive by calling timeout with 29 seconds remaining and the ball at the Indianapolis 32. Sanchez hit Edwards on the next play, a high pass to the right sideline.
Folk trotted on and won it.
"We've got to tip our hat to our offense. It was unbelievable," said Ryan, whose bravado made him a summer sensation in HBO's "Hard Knocks" series. "I mean, we totally dominated the second half offensively. On defense, we had to hold serve. Against Peyton, you're not going to stop him completely, but our guys played well enough to get it done and keep him out of the end zone. Our offense was just spectacular."