Rose ended with three birdies in his last five holes
Ian Poulter, Lee Westwood and Justin Rose all fell out of contention during a disappointing third round at Augusta.
Poulter started the day on five under but carded a bogey and double bogey in a round of 16 pars to end the day nine strokes behind leader Trevor Immelman.
Lee Westwood is a shot further back on one under after carding four birdies and five bogeys.
Rose, the joint first-round leader, endured a mixed round and is sitting on three over.
Rose, who shot 78 on Friday to effectively end his challenge, leaked three bogeys and a double on 11 before holing out from the greenside bunker on the short 16th.
"I was actually punching the air, not celebrating. The game's there but not being able to turn it into a score is frustrating," he said.
Rose, the world number nine, was talked of as a possible challenger before the tournament and a good contender to become the first European winner since Jose Maria Olazabal in 1999.
The story of the week has been on the greens for me
The 27-year-old was fifth last year after leading following the first round, and he also led after the first round in 2004 before falling back to 22nd.
But after ruining his chances on Friday he found scant consolation in the strong finish to his third round which included that shot at 16.
"There was more chance of hitting into the water than there was of holing it so it was a nice break, but they have been few and far between," he said.
"I've been shooting myself in the foot momentum-wise. It's happened to me before and it won't be the last time. That's the game.
"I hit the ball well off the tee and hit some good iron shots but I didn't put it together in a score.
"It really teases you, this golf course. When you play well you wonder what all the fuss is about but when you go at the wrong flag at the wrong time it bites you."
Poulter, who was joint third with Steve Flesch and Phil Mickelson overnight, had eight successive pars but dropped shots at the 9th and 10th after two shanks left him trouble.
The 31-year-old, who finished tied for 13th last year for his best Masters finish, could not get the shots back as he ended with eight pars for a 75.
"It's shame really," he said. "I got two bad lies. I hit a great drive on nine but it was across the downslope, just a horrible shot.
"I got a huge clump of mud on the ball at the 10th. It was above my feet and I'm trying to choke down on a four iron to cut it. It was a recipe for disaster really."
Westwood started with a bogey but worked his way back to four under, only to drop four shots coming home.
"The story of the week has been on the greens for me," he said. "It's just been woeful really. The birdies I made were tap-ins and I three putted three times.
"I'm just not making any long putts. I've been trying to figure out putting for 15 years so I'm hardly likely to figure it out on the Saturday at the Masters. This feels like one that's got away. Putting is a game within a game."
Augusta newcomer Nick Dougherty improved to three under with birdies at the 3rd and 6th but the 25-year-old hit three bogeys in the next four holes before dropping another shot at the 14th.
His 74 leaves him on one over going into the final day.
"I'm just trying to enjoy what I'm doing, being at Augusta and playing in my first Masters." he said.
"I had a good start but I didn't hit the ball how I wanted to and every time I got a bad shot I hit it into trouble. It could have been worse."
Australia's 2006 US Open champion Geoff Ogilvy, another pre-tournament fancy, carded a third-round 76 for six over, as did the 50-year-old Ian Woosnam, the 1991 champion.
Scotland's Sandy Lyle, Masters winner in 1988, amassed a 78 to prop up the leaderboard on nine over with South Korea's KJ Choi, the world number six.