Spieth, Partick Reed and Sean O'Hair couldn't be separated after 72 holes, the trio tied on 10-under, meaning extra holes would b required to crown the new champion.
Reed, who made a 30-foot putt of his own to book his place in the play-off was forced to make two top class saves to remain in contention, while O'Hair had a 12-foot birdie putt to win it on the second extra hole.
With all three players scoring par on the first two play-off holes, the competition headed to the par-3 17th. It was here that Spieth rose highest, sinking his long, pressure putt to take the victory.
Overnight leader Ryan Moore endured an up and down day, starting with a birdie before dropping out of the lead with a three-putt at the third. However, he was back out in front after holing out from 170 yards at the sixth to register an eagle.
He would then drop a shot at 10 only to birdie the 11th and 12th. A bogey on the 13th saw Moore's lead cut, and further bogeys at 16 and 18 saw Moore finish on eight-under, two back from the leading trio.
Spieth started strongly, with birdies and the first and second. Bogeys and five and six threatened to derail his charge, but the Texan reclaimed shots at the 13th and 14th to ensure he was in the mix when it mattered.
A strong back nine was the key for Reed in his round of 66. A lone birdie on the front nine was backed up by birdies on the 11th, 12th, 15th and 18th.
O'Hair too finished strongly after taking the turn in even par, with four birdies from the 11th to 16th doing the business for the Australian.
However, while Reed and O'Hair produced some quality golf to reach the play-off, they were unable to go the distance with Spieth.