The title was Garcia's seventh on the PGA Tour -- his first since 2005.
The 28-year-old Garcia shot a 1-under-par 71 and Goydos 74 in the final round, tying at 5-under 283 in regulation.
Garcia won with a tap-in par putt after Goydos drove into the water surrounding the island green at the 17th -- the first playoff hole.
The Spaniard collected $1.7 million.
"It's been a lot of work," Garcia said. "I feel like I've been playing well. Unfortunately I hadn't been able to come around and win. Everything was so hard. I'm thrilled the week is over and I managed to come out on top."
Goydos, who was bidding for his third tour victory, said his tee shot on the playoff hole "ballooned a little" before dropping into the water short of the green.
"That's the way it is sometimes," Goydos said.
Celebrity Breakups and divorces of 2014 [PHOTOS]