New England won on Tom Brady's 82-yard touchdown pass to Troy Brown with 5:45 left in the extra session.
The interception didn't appear that costly at the time because it came on third down and had the same result as a punt.
But the truth is this game never should have come down to the play because the Dolphins had two great opportunities to win before that.
And it was kicker Olindo Mare who proved the goat on this day.
He had a 35-yard field goal attempt blocked by New England's Richard Seymour in the last two minutes of the game. Seymour was allowed to get way to much penetration, but Mare didn't get the ball up quickly enough kicking from the dirt infield at Pro Player Stadium.
After the Dolphins won the overtime coin toss, a spectacular catch by Derrius Thompson gained 31 yards even though Thompson appeared to step on the sideline before the catch and he appeared to land out of bounds after making the catch.
Regardless, after robbing the Dolphins throughout the afternoon, the officials made up for it on that play and the Dolphins were in business.
A few plays later, they were in a position to win it with Mare lining up for a 35-yard field goal attempt, but again from the dirt infield.
Mare pushed the attempt wide right and the game continue.
It was the same type of game as usual for the Dolphins, with the defense playing very well and the offense scratching and clawing with few results.
The Dolphins turned the ball over twice on their first three possessions (a Fiedler interception and a Chambers fumble) but trailed only 3-0 after a 25-yard Adam Vinatieri field goal.
The Dolphins took the lead early in the second quarter after Jay Williams recovered a Brady fumble at the Patriots 16-yard line.
Five plays after that, Fiedler hit Chambers on a slant for a 6-yard touchdown.
The Dolphins defense got another turnover on the next series, with Larry Chester recovering a Kevin Faulk fumble. But after getting to a second-and-1 from the New England 3-yard line, the Dolphins had to settle for a field goal and a 10-3 lead.
The teams traded field goals to make it 13-6 before New England tied the game late in the third quarter on Brady's 24-yard touchdown pass to David Patten. The score culminated a drive that saw New England convert three third-down situations.
Neither team threatened in the fourth quarter until Mare's field-goal attempt in the final two minutes.
New England appeared poise to win the game in the final minute of regulation after the blocked field goal, but Terrell Buckley dropped Faulk for a 7-yard loss on a second-down play from midfield.
In the final analysis, though, the lack of offense wound up catching up to the Dolphins after Mare failed to deliver.