Dressed all in black, Woods got his day off to a wobbly start when he sent his opening tee shot deep left into the pines but he was unruffled and recovered to make par.
The American, who won the Masters in 2015, showed "remarkable prowess" and was in a "class of his own", says Sky Sports, as he hit five successive birdies on the back nine. He drove into the trees at the last but a sublime chip ensured only one dropped shot.
Finau's first Masters was in danger of being over before it even started when the 28-year-old suffered what appeared to be a gruesome ankle injury while celebrating a hole-in-one during Wednesday's Par Three contest.
"I feel like I won the two best major championships", he said, offering an apology to the other two, the U.S. Open and PGA Championship.
Woods nearly drove the green at the par-4 No. 3, pitched to about 10 feet and made the putt to set off a huge "Tiger Roar" at Augusta National.
But the biggest story of the round was Garcia.
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Well, not exactly. If it were that simple, Garcia might have a lot more prized possessions in his display case than the green jacket he won in a memorable back nine charge past year that included an eagle on the par-5 15th hole. "I looked forward to this week for a really long time, and to see the possibility of that slipping away; you know, I was really ecstatic to be walking to the first tee".
TIGER WATCH: Tiger Woods returned to the Masters for the first time since 2015 and shot a 73, leaving him seven shots off the lead.
"And I hit some good shots early, unfortunately they just didn't continue".
QUOTEWORTHY: "I know as well as anybody that anything can happen at Augusta National". "It's unfortunate, that's just what it is". Garcia shot an 8-over 13 on the hole.
SERGIO'S DEBACLE: For the second straight year, it looks like the defending champion will have nothing to do this weekend except hand out the green jacket to someone else.
Further birdie chances came on the 17th and 18th, but Woods was unable to make further progress.
It equalled the Tom Weiskopf in 1980 on the par-three 12th and Japan's Tommy Nakajima on the par-five 13th in 1978. Till then he was 2-over for first 14 holes and still stayed on to birdie the 16th and par the last two for an 81 and he was one spot above dead last.
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History has proven there are no guarantees at Augusta, but the betting money heading into Round 2 is the 2017 Masters champion Sergio Garcia won't come anywhere close to his second green jacket. "I'll always enjoy this tournament".
Garcia, so impressive in winning his first major previous 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.
Rory McIlroy was thrilled to post a 69 for a share of third after making three stunning par saves on the spin coming in.
"This is my best start a few years and it is such a hard course to play catch-up on".
Summing up the day, he said, "The putter did not work on the front nine and approach (shots did not work) on the back nine".
World No. 1 Dustin Johnson started with a one-over 73 while Justin Thomas had a slightly underwhelming 74 and Jason Day struggled to a 75. "Really any Major. I feel like I'm kind of one round down out of six, so I'm not getting ahead of myself".
He leads Matt Kuchar and Tony Finau by two.
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Woods was in danger of playing himself out of the tournament when he bogeyed the 11th and found the water with his tee shot on the 12th, but crucially salvaged a bogey after a mediocre pitch.