Former champion Watson held a five-shot lead after an eagle on the par-five second, but faded to a third round of 74 to finish five under par alongside 20-year-old compatriot Jordan Spieth.
Spieth only turned professional in December 2012 and was a 19-year-old special temporary member on the PGA Tour when he won the John Deere Classic last July, the youngest winner on Tour since 1931.
He went on to become rookie of the year and could surpass the absent Tiger Woods as the youngest Masters winner, as well as being the first player to win on their tournament debut since Fuzzy Zoeller in 1979.
Woods was 21 years, three months and 15 days when he won by 12 shots in 1997. Spieth will be 20 years, eight months and 17 days old on Sunday.
Matt Kuchar and Sweden's Jonas Blixt - also a Masters rookie - were a shot off the lead on four under, with 50-year-old Spaniard Miguel Angel Jimenez and Rickie Fowler three under.
England's Lee Westwood, seeking a first major title at the 64th attempt, was two under alongside Denmark's Thomas Bjorn and Jim Furyk, with US Open champion Justin Rose one under and Ian Poulter level par.
Defending champion Adam Scott struggled to a third round of 76 but was only six off the lead on one over.
Jimenez, who will make his Seniors Tour debut next week, only made the halfway cut with a shot to spare, but surged through the field with a best-of-the-week 66 containing seven birdies and just one bogey.
Jimenez is already the oldest winner in European Tour history, extending his own record by successfully defending his Hong Kong Open title in December, just weeks before turning 50 on January 5.
And the veteran Spaniard would become the oldest winner in major history if he could claim a green jacket on Sunday, eclipsing the record of Julius Boros, who was 48 years, four months and 18 days old when he won the 1968 US PGA Championship.
"That would mean a lot," said Jimenez, who held the halfway lead in the Open at Muirfield last year. "I have plenty of victories in my career and having a major in my career would be amazing. That would be the flower on top.
"If you are 50 it doesn't mean that you cannot play well. I'm still moving. I'm still flexible. I hit the ball longer than ever. I'm competitive you know. I don't want to commit to play the Champions Tour or any more senior events, apart from the Senior British Open, because I want to put myself in place too for the Ryder Cup. I would love to play the Ryder Cup.
"The main thing is that I'm doing what I like to do in my life and I'm enjoying it completely. It's my 26th year on Tour and probably some people say, that's so many years, that's got to be hard on the body. No, I love what I'm doing and I hope I'm still in the same condition for another 25. I'm not going to get bored of myself!
"I feel great. I feel fantastic. I like the feeling of the knot in my stomach. I feel that thing since Monday when I got here, it doesn't disappear. I love that kind of pressure. That's why I'm still competing."
Birdies at the third and fifth took Jimenez to the turn in 34 and the former Ryder Cup player birdied the 10th, 11th, 13th, 14th and 16th, with a bogey on the 12th his only blemish.
Westwood had failed to birdie any of the par fives in the first two rounds, but picked up shots at the second, eighth, 13th and 15th.
"Augusta is one of those places where I feel I can turn my game around," said Westwood, who took a two-shot lead into the final round of the Open at Muirfield last year but finished third.
"I know how to get round even if I'm not on my game. The course changes as the week goes on and Sunday afternoon is even more fun. Anyone within four or five of the lead will have a chance tomorrow, especially with the way the golf course is playing out here."
Notable figures from the third day's play:
5 - Bubba Watson held a five-shot lead after an eagle on the par-five second.
76 - Justin Rose's first-round score on Thursday. The US Open champion was just four off the lead after subsequent scores of 70 and 69.
70 - Score recorded by Jeff Knox, an Augusta member and non-competing marker for Rory McIlroy in the third round.
71 - McIlroy's score.
20 - Age of Jordan Spieth, who would become the youngest ever Masters champion with victory on Sunday.
50 - Age of Miguel Angel Jimenez, who would be the oldest winner of any major.
64 - Lee Westwood is seeking a first major title at the 64th attempt.
30 - Gary Woodland equalled the lowest front nine in Masters history before fading to a 69.
1999 - The last time a European player won the Masters.
14 - Number of shots separating leaders Spieth and Watson and former champion Larry Mize and Joost Luiten in last place.