Woods – four-time Masters winner – is four shots behind joint leaders Brandt Snedeker and 2009 winner Angel Cabrera, but remains optimistic of his chances of winning the green jacket.
“I never considered withdrawing from the tournament, the rules of golf say I can play so I went out and competed today,” said Woods.
“It was nice to make those three saves at the last three holes, that kept me in it.
“I’m four back and we’ll see where that puts me at the end of the day, but anything can happen on Sunday.”
Lee Westwood is the leading Brit going into the final day at Augusta with a third-round 73, and the Worksop-man fancies his chances of a maiden major.
“My chances are still pretty good, you can pick up a lot of shots round this golf course so I’ve still got a very good chance,” said the 39-year-old.
“It was very hard work out there. The greens are significantly firmer as they always are at the weekend.
“I could have shot under par but didn’t make enough of the par fives, not birdying two, so that’s the reason I’ve rolled a 70 into a 73.”
Showing signs of his 2011 Masters capitulation, Rory McIlroy endured a torrid day in Georgia, and with two sevens on the back-nine the Ulsterman admitted errors forced his third-round 79.
“I made a couple of bad errors on the front nine and I was still ok up until that point,” said the world number two.
“I hit a drive to the right on 11 and the wind switched on me and I took seven there and never really recovered.
“The same thing happened on 15 and it’s very small margins but you pay a big price for them.”
World number four Luke Donald expressed his frustration after a tough day at Augusta, in which he carded a 75 to put him two over for the championship.
“I felt like pulling my hair out the whole way round,” he said. “What’s making it difficult today is that the greens are a lot firmer and faster.
“I felt I could play pretty solid golf, but there were quite a few shots I was staring down that I hit short, and ended up making a bogey, instead of giving myself a chance.
“It was one of those days where the ball was just not going in the hole and it was a shame because the leaders don’t seem to be going too far ahead.
“It’s playing tricky out there, I would’ve loved to have posted something in the sixties today.”
Co-leader Snedeker carded a 69 to put him seven under going into the final day, but the American refused to belittle the magnitude of the job on his hands.
“To put on that green jacket I’ve got to do a lot of things tomorrow, and I’ve got to think really well as well,” he said.
“It was a great performance today, I really drove the ball well and left myself some good short par putts.
“I was able to be aggressive after my tee-shots and get some red numbers on the card which was nice.”
Adam Scott shot himself into contention with a third-day 69, and the Adelaide-born 32-year-old is hoping to be the first Australian winner of the Masters.
“It would be huge for an Aussie to win it, it’s amazing that the three of us are so close, it would be great for one of us to get over the hurdle but I hope it’s me,” he said.
“No-one really caught fire out there today, everyone is jockeying for position and I just slowly crept up on them with a really solid back-nine so I want to take that momentum and do the same tomorrow.”
Leaders: -7 Snedeker, Cabrera; -6 Scott; -5 Leishman, Day; -4 Kuchar.
Selected others: -3 Woods; -2 Westwood, E-Rose; +2 Donald, +5 McIlroy, Lawrie, Lynn; +9 Guan.
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BIOGRAPHY: Mohamed Salah