Justin Rose in a sudden-death playoff to cap a spectacular final round on Sunday.
On the first extra hole, Garcia made birdie while Rose had a bogey.
Garcia breaks a winless streak in majors, having played 73 tournaments without a victory before his breakthrough Sunday.
Both players missed short putts for birdie on No. 18 before settling for par to force a playoff.
Garcia brought some drama to the back nine by sinking an eagle on No. 15 to pull even with Rose, who birdied the hole.
Charl Schwartzel, the 2011 Masters champion, closed with a 68 to grab third at 6 under. In fourth at 5 under were Matt Kuchar, who aced the 16th and shot 67, and Thomas Pieters (68), who gave a strong run at becoming the first player since Fuzzy Zoeller in 1979 to win the Masters in his first try.
Jordan Spieth and Rickie Fowler, paired in the penultimate group, fell all the way down into a tie for 11th. Spieth, who finished second, first and second in his first three Masters, shot 75 while Fowler, who was trying to win his first major, shot 76.
Rory McIlroy never got untracked until late in the final round and shot 69 to finish in a tie for seventh; his pursuit of the career grand slam still ongoing. Phil Mickelson made an early run for his fourth green jacket but did himself in with a poor third round and finished in a tie for 22nd. Defending champion Danny Willett missed the cut, while world No. 1 Dustin Johnson was forced to withdraw before the first round with a back injury.