Snedeker, who was the hottest player on the PGA Tour earlier this year until a rib injury sidelined him, and Cabrera, who has won a Masters and a U.S. Open and nothing else in his tour career, shot 3-under-par 69s to share the top at 7-under 209.
Members of the Australian invasion held the next three spots. Adam Scott, seeking a chance at redemption after his shocking collapse in last year's British Open, carded a 69 for 210. Jason Day, the leader at the halfway point, bogeyed 17 and 18 for a 73 to tie Marc Leishman (72) for fourth at 211.
Woods, who almost didn't get a chance to continue his quest for a fifth Masters crown after a rules controversy that cost him a penalty but not a disqualification, made a pair of late par saves for a 70 and stayed in the hunt at 213.
"It started out different, obviously," Woods said of his day. "But I'm right there in the ball game. I'm 4 back with a great shot to win this championship."
Couples, who played in the last group with Day, played his final five holes in 5-over and had a 77 for a 216 total.
Snedeker, 32, winner of the 2003 U.S. Amateur Public Links championship at the now-closed Blue Heron Pines East in Galloway Township, N.J., did a terrific job of managing his game and staying patient despite diabolical hole locations and speedy greens.
The Nashville, Tenn., native, who tied for third here in 2008, started out with 12 straight pars before picking up vital birdies at 13, 15, and 16.
"You have to really be on top of your game because you can put the ball in some really bad spots," he said. "Patience is obviously the word of the week every week. Y'all get tired of hearing it, but I can't underscore how important that is around this place. I just stayed patient, waited for something good to happen, and it did."
Cabrera, 43, birdied the 16th and 18th holes to get himself into Sunday's final pairing with Snedeker. The eventual Masters champion has come out of the final group in 19 of the last 22 years.
The Australians, however, will be looming right behind. Scott might be the most motivated of the three, still carrying the memory of last year's British Open, where he blew a 4-stroke lead with four holes to play and lost to Ernie Els.
"If I'm in the same position I was in at the Open last year, then I'm obviously playing an incredible round, and I'll just be trying to finish the job," Scott said.
So will Snedeker, who left the property Saturday night with a ton of confidence.
"I've spent 32 years of my life getting ready for" Sunday, he said. "It's all a learning process, and I am completely, 100 percent sure that I'm ready to handle [it] no matter what happens. I'm going to be disappointed if I don't win, period. I'm not here to get a good finish. I'm not here to finish top five. I'm here to win."
Contact Joe Juliano at firstname.lastname@example.org. Follow on Twitter @joejulesinq.