Watson has held or shared the lead after 36 holes eight times on the PGA Tour, but only converted one of those into a victory at the Zurich Classic of New Orleans in 2011.
And the left-hander's task would not be made easier by the presence of defending champion Adam Scott on the leaderboard, the Australian recovering from three bogeys in the first five holes of his second round to lie just four off the pace.
Australian John Senden matched Watson's 68 to claim second place on four under, with Thomas Bjorn also returning a 68 to lie a shot further back alongside Scott, 20-year-old American Jordan Spieth and Sweden's Jonas Blixt.
"I was a little frail but patience came into it on the back nine and I just tried to remember all the good shots I hit on Thursday," said Scott, who is aiming to join Jack Nicklaus, Nick Faldo and Tiger Woods in winning back-to-back titles.
"It's good to be within shouting distance but Saturday is a big day for everyone. I would like to close the gap to feel in with a chance on Sunday."
Twenty two years after winning a green jacket, 54-year-old Fred Couples was five off the pace on two under, with Scotland's Stephen Gallacher and Welshman Jamie Donaldson a shot further back.
Watson, who adopted a month-old son with his wife Angie shortly before his Masters win in 2012, withdrew from his last event after blaming an opening 83 at the Arnold Palmer Invitational on his head being "all discombobulated" due to severe allergies.
But the 35-year-old from Bagdad, Florida, did claim his first PGA Tour title since the Masters in February, shooting back-to-back bogey-free rounds of 64 to win the Northern Trust Open.
"This year I'm trying to get the (green) jacket back," said Watson, who had five birdies in a row from the 12th to card a 68 and finish seven under par.
"Media attention is on the defending champion. You're asked all these questions, can you defend, how are you going to play, how are you going to do this? You have to give up the green jacket.
"For me I didn't know how to handle it the best way and so I didn't play my best golf last year. But this year I came in here with no media attention, somehow I was lost in the crowd a little so I could go about my practice rounds without much attention."
Pre-tournament favourite Rory McIlroy went in search of "something phenomenal" on Saturday to keep his faint hopes of winning the Masters alive at Augusta National.
McIlroy did not realise he had to par the last to make the halfway cut on the mark of four over par, but held his nerve from four feet to complete a disappointing - and admittedly unfortunate - 77.
That meant a total of 51 players - 50 professionals and Australian amateur Oliver Goss - qualified for the last two rounds and ensured McIlroy would be the first man out at 1015 local time, most likely playing with club member Jeff Knox as his marker.
"I just want to go out there and try to get off to a fast start," said McIlroy, who visited some seldom-seen parts of the course on the 10th and 13th, the latter after his ball hit a sprinkler and bounded into the azaleas which give the hole its name.
"Eleven shots back (of leader Bubba Watson) with two rounds to play is going to be nearly impossible to make up so I'm trying to shoot two really low rounds and see where that puts me at the end of the week.
"It will take something phenomenal to shoot something in the mid-60s and get myself back under par going into the last day. But I'm going to need to be two, three or four under par going into the last day to have any sort of chance."
McIlroy at least had an outside chance to cling onto, which is more than could be said for three-time winner Phil Mickelson, who missed the cut by a shot to make an early exit for the first time since 1997.
"I just had one bad hole there at 12," said Mickelson, who found a greenside bunker on the 155-yard par three, thinned his second shot into another bunker and then did exactly the same again.
"I keep making these triple bogeys, they're tough to overcome. I've actually played reasonably well for a majority of the holes and then the ones that I let slide I end up making a big number."
Asked if he would watch the final two rounds on television, Mickelson added: "It's an exciting tournament, so I probably will. It will kind of be my punishment."
Luke Donald, Sergio Garcia, Ernie Els and 2011 champion Charl Schwartzel also missed out by a shot, Donald shooting a second round of 70 but paying the price for an opening 79 which included a two-shot penalty for touching the sand in a bunker on the ninth after failing to escape at the first attempt.
Notable figures from the second day's play:
83 - The score from Bubba Watson's last round before the Masters. He withdrew after shooting it on the opening day of the Arnold Palmer Invitational, blaming severe allergies.
5 - Number of birdies Watson carded in a row from the 12th hole in his second round of 68.
51 - Thomas Bjorn's combined score over par in 10 previous Masters appearances.
51 - Number of players who made the halfway cut on four over.
110 - Combined age of former champions Fred Couples (54) and Sandy Lyle (56), who both made the halfway cut.
5 - Number of shots taken by Rory McIlroy on the par-three fourth hole, where his tee shot flew over the green and almost hit Adam Scott on the fifth tee.
1 - Only one of the six amateurs in the field made the halfway cut, Australia's Oliver Goss on three over after rounds of 76 and 71.
1 - Number of sprinklers McIlroy's shot hit on the 13th, sending his approach bounding into the azaleas which give the hole its name.
20 - Age of Jordan Spieth, who was not born when Couples won in 1992.