When they went back to 413-yard 18th again for the playoff, Koepka went first and drove into the water before taking his drop and leaving his approach short of the green. Garcia hit a drive of more than 300 yards and followed with a wedge to about 17 feet.
Garcia also won the 2004 AT&T Byron Nelson and is the first two-time winner in the 34 tournaments since the event moved to TPC Four Seasons in 1983.
Koepka closed with a 71.
Matt Kuchar was a stroke out of the playoff at 14 under after a 65.
Spieth, the No. 2-ranked player in the Official World Golf Ranking, had two bogeys in his first five holes Sunday and went on to shoot 74. He finished tied for 18th at 10 under.
Koepka, who opened the final round leading by two strokes over Spieth, was at 17 under before the back-to-back bogeys that dropped him even with Garcia. Koepka hit each of his first two shots into the rough at both the 14th and 15th holes.
Then after his drive at No. 18 went into the right rough, Koepka still had a chance to win without a playoff when he made a nice shot to the green. But his 16-foot birdie chance curled just under the cup.
Garcia was 15 under for the third time in his final round when he made a short birdie putt after a nice chip shot at the par-5 16th. He had a pair of 12-foot birdie chances after that, but the ball stopped short at the par-3 17th and curled around the cup at No. 18.
In his 301st PGA Tour start, Garcia improved to 5-6 in playoffs and got a check for $1,314,000. Koepka was in his first playoff in his 55th tournament, a year after his only victory in Waste Management Phoenix Open.
Spieth first played in the AT&T Byron Nelson as a 16-year-old six years ago, and the Dallas native missed his high school graduation ceremony the following year after again making the cut there as an amateur.
Six weeks after his misery at the Masters, and a week after missing the cut at THE PLAYERS Championship in his only other tournament since that blown five-stroke lead on the back nine when trying to win at Augusta for the second year in a row, Spieth was pretty much out of contention at home after his two early bogeys.
That came on the same day that third-ranked Rory McIlroy won the Irish Open, his home tournament where he had struggled over the years.
Despite the 8,000 bobbleheads given away Saturday, the huge crowds watching his every move and his picture plastered everywhere at TPC Four Seasons, Spieth insisted several times that this week it felt like a normal tournament.
He also kept talking about how uncomfortable he felt with his ball-striking despite being near the top of the leaderboard. The erratic swings finally caught up with him in the final round.
After hitting his first two shots at No. 8 into the rough on way to his third bogey of the day, Spieth was 12 under and already four strokes behind Koepka. About that same time, Garcia was finishing a streak of three consecutive birdies at Nos. 5-7 to get to 15 under for the first time.
Koepka was 17 under after his last birdies of the day, at Nos. 7 and 9.