The 2017 Masters marked his 74th major appearance.
Three-times Masters champion Phil Mickelson birdied the first two holes but a double-bogey at the third put the experienced American left-hander on level par.
Rose and Garcia started out tied for the lead. Rose ended up bogeying the hole, while Garcia notched a birdie.
Garcia fell two shots behind after bogies at the 10th and 11th holes, but got one back with a birdie on the 14th.
Both Garcia and Rose hit good drives on the 18th hold, then both missed short makeable putts to force what turned out to be a one-hole playoff.
Garcia hit a brilliant approach at the 14th to close the gap to one then the highlight of the day came at the par-5 next when hit an 8-iron second shot to 12 feet and drained the eagle putt.
Garcia, who once complained the golf gods conspired against him when he lost a playoff in the 2012 British Open, had the gods on his side Saturday in Amen Corner.
Rickie Fowler and Charley Hoffman birdied the second hole to head the U.S. Masters third-round leaderboard at a sun-kissed Augusta on Saturday.
But while he has broken through into the ranks of major winners with his 2013 US Open win, and went on to claim last year's Olympic title, Garcia had failed in 73 attempts before Sunday to win a major title. Fowler fired a 1-under 71 that leaves him one shot off the lead, and Hoffman is two shots back after carrying a four-stroke advantage into Friday's round. And his final-round 75 tied his worst 18-hole score at the Masters, too.
"It is wonderful. To do it on his [Ballesteros'] 60th birthday and to join him and Jose Maria Olazabal, my two idols in golf, it is something incredible", said Garcia before accepting the Green Jacket from last year's victor Danny Willett in Butler Cabin.
Both Rose and Garcia shot 69 on Sunday.
"I'm certainly not getting ahead of myself", Rose said. Bogeying the last three holes didn't help.
The 28-year-old has had some big moments in golf, winning prestigious tournaments like the 2012 Wells Fargo Championship and The Players Championship and Deutsche Bank Championship in 2015. "I'm going to need something like that to have a chance tomorrow", McIlroy said.
As they entered the back nine Garcia started to crack with back-to-back bogeys, and fans covering their eyes as they feared he would let another major slip through his fingers. "Even after the two bogeys, I knew I could still do it". The sudden-death playoff was a bit anticlimactic, pretty much decided when Rose drove behind a towering magnolia tree right of the fairway, forcing him to punch out and hope he could somehow make par.