Three clear when he ran up a seven on the eighth - his third shot was stuck up in a palm tree - Quiros aced the 161 yard 11th to get back to 11 under par.
South African James Kingston and Dane Anders Hansen were in second place, with Rory McIlroy and Lee Westwood among those three back and Tiger Woods part of a group four adrift.
Woods had only five holes to go, though, and Westwood's chances appeared to have gone when his drive on the 17th was lost in the trees and he had to go back to the tee.
Sergio Garcia, playing with Woods, shared top spot after an opening birdie, but fell back into the pack with a triple bogey at the ninth.
Quiros received treatment on his right arm before playing the 14th and as he three-putted for bogey there Hansen made an eight footer for eagle at the 13th and leapfrogged the Spaniard into a one shot lead at 11 under.
Westwood, whose ball on the 17th was up a tree like Quiros at the eighth, double-bogeyed and had another six on the long last after hitting his second into the lake. A 72 left him five under and only 16th.
Quiros birdied the 16th from ten feet to get back on terms and then led on his own again when Hansen bogeyed the short 15th.
Woods pitched into the lake on the last and a double-bogey seven gave him a 75, the same as Garcia. They were down in 20th spot.