Garcia, so impressive in winning his first major last year, was two-over-par playing the par-five hole and in a good position for a birdie as he played his 200-yard approach shot.
But after spinning back into the water with his first effort, the Spaniard then saw four further efforts from the nearer drop zone suffer the same fate.
His sixth effort found the green and he holed the putt for the octuple-bogey 13, the joint worst score on any hole at the Masters and the highest on the 15th, his title defense in ruins after a nine-over 81.
'It's the first time in my career I make 13 without missing a shot," said a rueful Garcia. 'I felt like I hit a lot of good shots, but the ball just didn't want to stop. It's unfortunate, that's just what it is."
If Woods is to cap his astonishing comeback with a fifth Masters title he will still have to produce something special over the next three days, particularly as late starter Jordan Spieth tore through the back nine to lead on six-under 66.
Three-over-par through the 12th, a fighting finish over the closing holes gave him hope he can still mount a challenge.
"I played well, but made a few mistakes here and there and didn't take care of the par fives," said Woods.
"I fought hard and had a little bit of a comeback on the back nine.
"There's still a long way to go," he added.
Only once in 20 attempts has Woods broken 70 in his first round at the Masters, but he showed early promise with a birdie on the par-4 third to go into red figures.
But instead of kick starting his round it stalled immediately with back- to-back bogeys on the fourth and fifth to go one over par.
He maintained that position through the turn, but the tough stretch of holes known as Amen Corner saw the former 14-time major winner slip through the field.
A wayward drive on the 11th cost him another dropped shot, while his tee shot on the short 12th found Rae's Creek.
It might have been worse, Woods draining a 20-foot putt for just a bogey to go three-over-par for his round.
Hopes were raised ahead of the Masters after the 42-year-old Woods finished 12th, second and fifth in his last three starts on the PGA Tour and he showed evidence of that improved form with fighting birdies on the 14th and 16th to fight back.
Further birdie chances came on the 17th and 18th, but Woods was unable to make further progress.
His score was holding up well until a rush of birdies by 2015 winner Spieth put it into perspective.
Five in a row through the 17th saw the Texan go two clear of his nearest chasers Tony Finau and Matt Kuchar, who both carded 68s.
Spieth, who also eagled the 8th, had to show good touch to only bogey the 18th after finding trouble off the tee, but his was a fine 66 in benign evening conditions.
Finau, who badly turned his ankle while celebrating a hole-in-one in the par-3 contest Wednesday, made a scarcely believable recovery from an injury that threatened his participation to challenge for his first major victory.
'It was a freaky incident," he said. To say it was scary night was quite an understatement, but obviously from that point to where I stand to day is nothing short of a miracle."
Bay Hill winner Rory McIlroy, seeking his career grand slam by winning the Masters, was one of seven players on three-under 69, holing a number of impressive putts down the stretch.
Wood's great rival, 47-year-old Phil Mickelson, who revived his career with a brilliant victory in the WGC event in Mexico, is also in contention after a two-under 70, which might have been better but for missing a short birdie putt on the final green.
But it was an indifferent day for the world's top two ranked players, with No.1 Dustin Johnson finishing on the same mark as Woods and Justin Thomas on two-over.