Gonzalo Fernandez-Castano had the round of the day, a 5-under 67, and moved into second. He's tied with Jamie Donaldson, who was the first-round co-leader with Rose, for second at 7-under. Donaldson had three bogeys Friday in a 2-under 70.
Gareth Mulroy, who shot 68 Friday, and Joost Luiten, with a second-round 69, are tied for fourth at 5-under 139. Eight players are at 4-under.
Rose, playing the second nine of the Abu Dhabi Golf Club first Friday, opened with six pars. After a birdie at the 16th he had three more pars. He went birdie-bogey-birdie over holes 2-4. A birdie at the 456-yard, par-4 nine gave him sole possession of the lead.
McIlroy posted his second straight 3-over 75 and missed the cut by four strokes.
Woods also shot 75 for a 36-hole total of 3-over. Woods, who had a triple-bogey 7 at the fifth hole, had three consecutive birdies over Nos. 14-16 to get to the cut line of 2-under but then had a bogey at the par-4 17th and missed the cut.