McIlroy and Quiros each had four birdies and three bogeys in posting 1-under-par 69s and are at 7-under 133 for the tournament.
They have a one-stroke lead over Panupol Pittayarat and Richie Ramsay, who are at 6-under 134. Pittayarat, whose second round included three birdies and an eagle, was one of three players to fire a 5-under 65. Ramsay had five birdies and a bogey for a 66.
Pariya Junhasavasdikul and Danny Lee had the other 65s and pulled into a tie for fifth with Miguel Angel Jimenez, who shot 70,
David Horsey, who shared the first-round lead with McIlroy and Quiros, had a double bogey 6 in the 18th hole and two bogeys and two birdies in dropping to 4-under for the tournament with a 2-over 72.
McIlroy was 3-under after 15 holes Friday but had bogeys on 16 and 18 to fall back to the pack.
Quiros, playing the back nine of the Hong Kong Golf Club first, made the turn at 3-under but bogeys at 1, 5 and 9 -- despite a birdie at the sixth hole -- left him tied with McIlroy.