One behind the leading trio of Anders Hansen, Thomas Aiken and Rory McIlroy, Quiros used his length to his advantage to eagle the 351 yard second and birdie the long next.
They were holes Tiger Woods dropped shots at, while joint overnight leader McIlroy bogeyed the first after a poor drive and slipped to joint sixth.
Quiros was ten under par, two ahead of Aiken, France's Jean-Baptiste Gonnet and Swede Fredrik Andersson Hed, who holed a 25 footer for birdie at the par three fourth.
There were still 17 players within four shots of the lead, amongst them Europe's new Ryder Cup Captain José Maria Olazábal, who was four under on the day with one hole remaining and six under overall.
Quiros went three clear with another birdie on the fifth, but then came a nightmare at the 459 yard eighth.
After driving into the desert scrub he took a penalty drop, but his third shot then flew into a palm tree in front of him and stuck in branches 15 feet up.
Able to identify it with the binoculars of European Tour Chief Referee John Paramor, he took another penalty drop underneath and ran up a triple bogey seven.
The lead as a result switched to South African James Kingston on nine under following his birdies at the tenth and 11th, but now it was wide open again.
Woods, turning in a one over 36, was only three behind and both McIlroy and Lee Westwood were part of a group just two back, but Sergio Garcia had a triple bogey of his own on the ninth to be five adrift.
Quiros came straight back with a birdie on the demanding ninth - and then dramatically holed-in-one at the 161 yard 11th.
The third ace of the week - David Howell and Raphaël Jacquelin made ones on the seventh - put him two ahead of Kingston and Dane Anders Hansen, but Woods, having birdied the 11th, drove into sand on the next and bogeyed to fall to joint 12th, five back.