The loss was a blow to the Seahawks' hopes of making the post-season as they slip to 6-5 in the NFC West despite an impressive performance from their rookie quarterback Russell Wilson.
Looking composed, quick on his feet and alert, Wilson threw for 224 yards and two touchdowns, with an additional 38 yards rushing.
Miami (5-6), which ended a three-game losing streak, opened the scoring with a 21-yard run from Reggie Bush in the second quarter.
But Seattle responded when Wilson wriggled free and lobbed a gentle three-yard pass into the corner of the end zone for Anthony McCoy, to tie the score at the half.
The Seahawks got in front when Wilson, after making a key 20-yard rush to get his team into the red zone, threw a four-yard pass to Michael Robinson.
The crucial moment in the game came with just over eight minutes remaining on the clock in the fourth when Ryan Tannehill's throw into the end zone was intercepted.
But the officials spotted Seattle free safety Earl Thomas had hit Tannehill after his throw and the penalty gave the Dolphins a first-and-goal, leading to Daniel Thomas's three-yard rushing touchdown.
Miami didn't stay on level terms long though as the lightning fast Leon Washington promptly returned the kick-off 98 yards to put Seattle up 21-14.
The Dolphins kept finding ways to bounce back though. Tannehill found Charles Clay open in the right corner of the end zone with a 29-yard touchdown pass to level the score.
With the ball in his hands one final time, rookie Tannehill led an impressive seven-play, 65-yard drive culminating in Carpenter's game-winning kick.