Both Garcia and Justin Rose held the lead during the closing 18 holes on Sunday but after Garcia missed a five-foot putt to win on the last, he recovered to make birdie at the first playoff hole.
The triumph was regarded as the Spaniard's make-or-break moment after a number of missed opportunities at previous Major tournaments, but he has insisted that he had never felt so relaxed.
The 37-year-old told reporters: "I felt like this course was probably going to give me one Major. That thought changed over the years as I started feeling uncomfortable on the course but I came to peace with it and accepted it.
"I knew I was playing well. I felt the calmest I ever felt in a Major. Even after a couple of bogeys I was still positive that there were a lot of holes I could get to. I am so happy."
The win for Garcia also removes his tag of being the player with the third most Major appearances without success.