McIlroy went out after slumping to a second successive three-over 75 on his debut with his new Nike clubs and Woods suffered the same fate after being handed a belated two-shot penalty for a bizarre rules infringement at the fifth hole.
Rose (69) almost crept under the radar as he went one stroke clear of fellow Briton Jamie Donaldson (70), Dane Thorbjorn Olesen (69) and Gonzalo Fernandez-Castano of Spain (67) at the tough Abu Dhabi Golf Club layout.
World number five Rose has had his share of back trouble over the years but he said the problem had been eased by new footwear.
“When you do as much walking as we do I really believe these softer soles, and the flexibility they give, help me,” the 32-year-old Englishman told reporters after finishing with an eight-under total of 136.
“I don't have a great hip rotation so if I wear a really rigid shoe I can't turn as well on it and therefore my lower back takes a bit of pain."
Rose's steady climb up the world rankings, his excellent performance at last year's Ryder Cup and some victories on the U.S. PGA Tour have given his confidence a huge lift.
"I think there's a difference in how I feel about my game and how I trust my game," he said. "I believe that any tournament I tee up in, I can win.
"Often you tell yourself that but really believing it is a different kettle of fish."
Rose said his iron play was faultless on Friday as he mixed four birdies with a solitary bogey.
"I felt like I hit the ball pin-high an awful lot today and that tells you that you are swinging the club great," he added.
“Conditions were absolutely perfect today. There was maybe a five-mph wind that just puffed up for the last couple of holes but really nothing to get in the way of low scoring."
Woods produced an erratic effort although he was ultimately undone by tournament referee Andy Mcfee.
The 14-times major winner made a dreadful start, dropping strokes at three of the first four holes before making another bogey at the fifth.
Six holes later Mcfee informed Woods he might have to sign for a triple-bogey seven rather than a bogey five.
Woods had struck a wayward shot into a desert bush at the fifth and, after consulting playing partner Martin Kaymer, the pair agreed he should be allowed a free drop because it had become imbedded.
The regulations, however, allow for a free drop in such circumstances only if the ball has finished anywhere but in sand and Woods was therefore handed his penalty at the end of the round.
“It’s tough because I didn’t get off to a good start but I fought and got it back,” the 37-year-old American said after eventually posting a three-over-par 75 for a three-over tally of 147 to miss the cut by one stroke.
“I was right there and I felt if I was even-par overall I had a chance going into the weekend, being only eight back of the leader. Evidently it wasn't enough.”
Woods had produced a scorching run of five birdies in nine holes from the eighth, including three in a row to the 16th, but his rally proved in vain.
McIlroy , playing alongside Woods and Kaymer, was as disappointed as the American after he also failed to qualify for the last two rounds.
“It was pretty much the same as yesterday,” said the Northern Irishman. "When you don’t hit the fairways on this course you can't score.
“I didn’t drive the ball well, I didn’t putt well again and my iron play wasn't anywhere near the standard that is usual for me. All aspects of my game were off.
“It’s the first week,” he said, referring to his new clubs, “so I wouldn’t read too much into it.
“I’ll work on the range for a few hours tomorrow and try to clear a few things up with my coach,” added McIlroy who now plans a four-week break from competitive golf.