"I came here for a reason and we accomplished that reason and certainly have some momentum going into next week," said Spieth after some had questioned his returning to the site of his first PGA Tour win in 2013 to play the week before a major championship.
The victory was the world number two's fourth of the season and the 21-year-old moved within one victory of tying Tiger Woods for the most wins on the PGA Tour before age 22, the Tour said.
Playing the 18th hole for a third time in a half-hour, Spieth, who finished regulation with a three-under 68, used a short par putt for the victory over the 46-year-old Gillis, who was making his 172nd career PGA Tour start.
Gillis, who shot a 64 in regulation, saw his chance for victory end when his approach shot on the second playoff hole found water.
He still earned the final qualifying place for the British Open, which starts on Thursday at St. Andrews.
Spieth, who ovecame a poor start to the day, could have won the tournament in regulation but missed a 30-foot putt.
He had another putt narrowly miss on the first extra hole, which both players parred after ending regulation at 20-under-par.
"It's extremely satisfying to have stretches where I played poorly and still came away with a win," said Spieth.
"Not the best start, but certainly OK with the outcome," the overnight leader told CBS.
American Zach Johnson (65) and New Zealand's Danny Lee (67) tied for third at 19-under 265.
Spieth had gotten the round off to an inauspicious start when he bogeyed the first and third holes before recovering to make the turn at even par.
After a bogey on the 11th he birdied four of the next five holes from 13th on to force a playoff a day after a sizzling 61 put him atop the leaderboard.
Gillis surged into the lead with five birdies in his first six holes and added another at the eighth before giving a stroke back with a bogey at the ninth.
He added more birdies at the 10th, 12th and 15th before a bogey at 16 gave Spieth a chance.
(Reporting by Gene Cherry in Raleigh, North Carolina; Editing by Greg Stutchbury)
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