A log-jammed leaderboard, featuring five players one stroke off the pace, sets up a fascinating weekend for the first Major of the year with 52-year-old Couples, winner here 20 years ago, cast in the role of nostalgist's underdog.
McIlroy, the world number two and US Open champion, shot a composed two-under-par 69 to move within a stroke of the lead but the man he was presumed to be duelling with at Augusta - four-times Masters winner Woods - came close to imploding.
Woods pushed his tee shot right into the bunker on the 16th and hurled his club to the floor before kicking it away in a flash of anger and frustration.
There was no shortage of grimacing and muttering from a tired and unhappy looking Woods as he battled through the final holes, struggling but avoiding a total meltdown that would have left him missing the cut.
After opening with birdies on two of his first three holes, Woods had five bogeys the rest of the way and posted a three-over 75 that left him eight shots back of the leaders and three shots from missing the cut.
But the raw data does not capture the disappointing display from a player who, fresh off his first PGA Tour win in 30 months, was made bookmaker's favourite this week.
McIlroy started the day four shots off the pace but the Northern Irishman made a solid start with three birdies on his first seven holes, including a 35-foot birdie putt on the par-three fourth.
He briefly had a share of the lead, after a birdie on the 15th, but slipped back after he bogeyed the 17th hole.
Spain's Sergio Garcia looked set to join the American duo atop the leaderboard but bogeyed the par-four 18th to finish at four-under 68, a shot off the pace along with Lee Westwood (72), Louis Oosthuizen (72), McIlroy and Bubba Watson (71).
Couples mixed seven birdies with two bogeys for a five-under-par 67, matching the second round score he shot at Augusta National in 1992 when he won the Masters.
"I feel like I know every inch of the course. I've played 28 years here and today was really a magical day," said Couples.
"I'm going to be right there with everybody Saturday and Sunday, well, Saturday for sure."
Overnight leader Westwood had parred his first 10 holes and produced two birdies on the back nine but undid a lot of his work on the final hole where he three-putted for a double bogey.
South Africa's Oosthuizen, who began the day tied for second, had a rough start to his round with a double-bogey seven on the second hole before a strong finish that included three birdies on his final five holes.
But the surprise face among the leaders was Couples, who plays mainly on the senior Champions Tour but showed has vast understanding of the course where he won his only Major.
The veteran, who started the day in a share of 29th place, had two bogeys and five birdies on the front nine and was flawless the rest of the way, making birdies at the 15th and 16th to move to five-under.
Dufner has recently made a habit of getting into the lead in the first half of tournaments only to fade at weekends but he will be looking to go one better than at last year's PGA Championship where he lost in a playoff to Keegan Bradley.
South African Charl Schwartzel, who won last year's Masters title by two shots when he became the first champion to birdie the last four holes, was eight shots back after a three-over 75.
Among those missing the cut were nine former Masters champions and reigning Open champion Darren Clarke.
Australian Jason Day, joint runner-up last year, withdrew from the event with an ankle injury after seven holes of his second round.