Perry (70) and Cabrera (69) finished on 205, two strokes ahead of Chad Campbell (72) of the United States.
A double-bogey five at the 16th dropped Campbell, the overnight co-leader with Perry, from a share of the lead.
Jim Furyk fired a four-under 68 to take fourth place on 208, one better than fellow American Steve Stricker (68).
Shingo Katayama of Japan, bidding to become the first Asian to win a men's major, was tied with South African Rory Sabbatini and American Todd Hamilton on 210.
Tiger Woods and Phil Mickelson, numbers one and two in the world, were lurking on 212 and will be paired together in Sunday's final round.
"I think for me to have a chance it will take a 64 or 65," Mickelson told reporters. "But I think it's out there."
A violent storm that swept through Augusta on Friday night dumped 1 1/4 inches (3.17cm) of rain on the course, making greens receptive to approach shots although the players also had to contend with breezy conditions.
Greenside Bunker
Perry, 48, trying to become the oldest winner of a major championship, jockeyed for the lead with U.S. Ryder Cup team mate Campbell for most of the round before the latter took two shots to get out of a greenside bunker at 16.
Cabrera, the 2007 U.S. Open winner, came back from a three-putt bogey at the first hole to grab a share of the lead with a 12-foot birdie putt at the 17th.
The stocky Argentine said winning his first major at Oakmont gave him the confidence he needed as he attempted to become the first South American to win the Masters.
"What I learned is I can win big tournaments," said Cabrera through an interpreter.
Cabrera, after going 68-68-69, is also on target to become the first player to post four sub-70 rounds in the tournament.
Perry, who lost a playoff for the 1996 U.S. PGA Championship to compatriot Mark Brooks, declined to answer when asked how much it would mean to win his first major.
"I'm not going to answer that until it actually happens," said Perry, who overcame a wobble at the start of the Amen Corner holes when he bogeyed the 11th and 12th.
"This golf course is too demanding. I had a tough day out there, I was struggling. I was nervous but settled down and got into the round.
"I'm looking forward to seeing what I've got. I'll answer that question tomorrow if I actually get to put that Green Jacket on."