McIlroy and Horsey both had six birdies while Quiros had an eagle and four birdies in taking a one-stroke lead over Miguel Angel Jimenez.
Jimenez was at 6-under for a while Friday but a bogey at No. 15 cost him a share of the lead.
Darren Beck and Gareth Maybin are tied for fifth at 4-under and Marcus Fraser is alone at 3-under.
McIlroy, playing the second nine of the Hong Kong Golf Club first Thursday, made his turn at 2-under after birdies at Nos. 14 and 16. His approach at the first hole ended up 3 feet from the hole for birdie and he followed that with another at the second hole. Birdies at 5 and 6 put him in the lead.
Horsey opened with a birdie at No. 1 and also birdied the third hole. He closed the front nine with a birdie at 9 and opened the second with a birdie at 10. A birdie at the 12th hole pulled him within one of McIlroy and a closing birdie at 18 tied him for first.
Quiros had front-side birdies at 3 and 7 but jumped up with a birdie at 11 and an eagle at the par-5, 529-yard 12th hole. He also birdied the 18th hole.
Swim Week Miami Beach 2014 [PHOTOS]