Cabrera, Snedeker share lead
Snedeker kept his cool in the suffocating pressure of Augusta National to shoot a flawless three-under par 69 to finish the day at seven-under.
He was joined at the top by Cabrera, the 2009 Masters champion, who drained a birdie putt at the last hole for a 69, igniting a huge roar from the greenside galleries that echoed around the Georgia course.
Adam Scott was third at six-under after also signing for 69, one stroke ahead of fellow Australians Jason Day (73) and Marc Leishman (72), raising hopes the winner's green jacket could finally be heading Down Under after years of near-misses.
Matt Kuchar (69) was at four-under, just one ahead of South African Tim Clark, who shot the best round of the day with a 67, and Woods, who was almost disqualified for a rule infringement.
"I'm right there in the ballgame," Woods said after shooting a 70. "As of right now I'm four back with a great shot to win this championship."
Tournament officials used their discretionary powers to allow Woods to remain in the championship for an incident in Friday's second round.
The world number one could have been disqualified for an illegal drop at the 15th hole but the Masters competition committee took a lenient approach, slapping him instead with a two-shot penalty.
"I understand and accept the penalty and respect the committee's decision," Woods said in a statement before starting his round.
The decision not to disqualify Woods triggered an instant debate around the golfing world, with players and fans divided over whether he had gotten off lightly or should have withdrawn himself.
But for the players on the course, it was business as usual as they tried to make up ground on what is traditionally known as moving day.
Snedeker, ranked fifth in the world, made a steady start, parring his first 12 holes before reeling off three birdies on the back nine to join Day in the lead.
The Australian, who finished joint runner-up with Scott two years ago, led by a shot overnight.
Like Snedeker, he also parred his first 12 holes then birdied the par-5 13th but slipped up with bogeys on each of the last two holes.
Scott, who threw away a four-shot lead with four holes to play at last year's British Open, gave himself a chance for redemption with a tidy round while Leishman, who shared the lead at times throughout the day, made a bogey at 17 to finish level with Day.
Veteran American Fred Couples started the day a shot behind but lost touch when he carded a 77 while Rory McIlroy's charge crumbled when he shot a 79 that included a triple bogey and a double bogey on the back nine.
"I was only a few off the lead going into seventh hole today and then all of a sudden I play seven through 11 in five over par and basically my chances in the tournament are gone," said McIlroy.
The defending champion, American left-hander Bubba Watson, made six birdies but handed back four shots with a pair of bogeys and a double to finish the day at two-over.
"I have to shoot a real low one tomorrow to have a chance," said Watson.
"But I will come out tomorrow and just enjoy the walk as my last day as defending champ and try to shoot a decent number."
China's teenage sensation Guan Tianlang, the feel-good story of the tournament, once again wowed the galleries with his clever shotmaking and nerves of steel that belied his tender years.
"I get to play with all the top players on the weekend," the 14-year-old said after his 77. "It's great for me, and I think I had a pretty good run in the first two days, and today feels pretty good."