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.