Phil Mickelson was five shots off the pace in his bid to repeat as Masters champion and Tiger Woods was six behind, both of them looking up at a collection of young players seeking their first major title.
Of the top 12 players on the leaderboard at the Augusta National Golf Club, just three have captured one of golf's biggest championships.
The 21-year-old McIlroy, who led after the opening round at last year's British Open, was the only player in the 99-man field to complete his round without a bogey while firing a 7-under 65.
Quiros, 28, used his enormous length off the tee to birdie four of the last six holes and tied McIlroy while playing in the final pairing of the day.
K.J. Choi, who appeared likely to become the first Asian to win a major title, and Y.E. Yang, who beat Choi to that honor by capturing the 2009 PGA Championship, were tied for third at 67.
Last year's PGA Tour leading money winner Matt Kuchar and Ricky Barnes both had a 68 while Sergio Garcia, Geoff Ogilvy and former Masters champion Trevor Immelman were among those at 69.
Mickelson scrambled throughout the day en route to a 70 and he did not bogey a hole until he missed the green and was unable to get up and down at the 18th. He saved par at both the 10th and 13th after driving deep into the pine trees, but he missed a series of birdie chances on the front nine.
Woods played the kind of unspectacular round that has become his trademark since his personal life unraveled at the end of 2009. He has not won a tournament since and has fallen to seventh place in the world rankings.
Both McIlroy and Quiros are making their third Masters appearance and neither had been in the 60s before Thursday. The 65 posted by Quiros was 10 strokes better than he had shot in his four previous rounds at Augusta National.
Martin Kaymer, ranked No. 1 in the world, struggled to a 78. Second-ranked Lee Westwood, who played in the same pairing with Kaymer, had a 72.