The 21-year-old led by two shots overnight, but was overtaken by fellow American Tom Gillis who shot seven-under 64 to finish on 20 under.
But a birdie from the Masters and US Open champion on the 17th, then a par, took him into a play-off with Gillis.
Spieth clinched victory on the second hole, for his fourth PGA win of 2015.
On Saturday he shot a career best 10-under 61, having begun the tournament poorly with a 71.
During the final round, a bogey on the 11th coupled with Gillis's charge saw him lose ground. But a final flourish over the last two holes, took the tournament into a play-off.
Spieth lipped out of the first play-off hole with victory in sight, but made no mistake on the next after his opponent found the water with his approach.
The consolation for Gillis is that he secured the final spot at next week's Open at St Andrews.
Spieth won his first PGA Tour title at the same event two years ago and is attempting to become the first player since Ben Hogan in 1953 to win the first three majors of the year.
-20 J Spieth, T Gillis; -19 Z Johnson, D Lee (NZ); -18 S Stroud, J Thomas, J Wagner; -16 D Summerhays, S Wheatcroft, W Wilcox, K Chappell.
