The 21 year old McIlroy shone with a seven under par 65 and will go into the second round joint leader with big-hitting Spaniard Quiros.
Two behind in third are Koreans Y E Yang and K J Choi, while Tiger Woods started with a 71 to be in a tie for 24th and defending champion and favourite Phil Mickelson with a 70 for joint 14th spot.
Despite some adventures three-time winner Mickelson, who made a late decision to drop a second driver from his bag, was heading for the only bogey-free round other than the one by McIlroy until he went into the crowd at the last and failed to get up and down.
Last man out Quiros, though, birdied the 18th to knock an amazing ten strokes off his previous best score on the course.
He said: “It’s difficult to believe – it has to be up there with my favourite rounds of all time, because my best score here before today was a 75. So I played very well, and the best club in the bag was my putter.
“On the 17th, I made a birdie putt which if it hadn’t caught the hole, I probably would’ve been chipping to save par. So I holed many good putts and played very well, but it’s only the first round of the week.
“Hopefully I can play well tomorrow, and make the cut for the first time. It would be a big improvement on the two previous years, and would definitely give me a shot of confidence.”
McIlroy's display brought back memories of his Major record-equalling first round 63 in The Open Championship at St Andrews last July.
But that is where the Northern Irishman hopes the comparisons end - McIlroy followed it with an 80.
He said: "It was not as explosive or as spectacular as St Andrews, but it was very solid and it's a great start."
The best at The Masters Tournament, in fact, since Greg Norman's 63 in 1996.
"I felt as if my game's been really good all season and after working on my game in Florida for 10 days with my coach Michael Bannon I feel very comfortable.
"I'm still relatively inexperienced, but I feel I am pretty quick learner. There's no substitute for experience and I've still got a lot of learning to do, but I am getting there.
"It was nice to see a few putts drop in as well and hopefully I can build on it.
"I think what happened at St Andrews will be a massive help. It was a very valuable lesson in my development as a golfer."
After saving par from the fairway bunker at the first he birdied the next three from two, five and 20 feet, and made a ten footer on the ninth to turn in 32.
The 505 yard 11th is probably Augusta's toughest hole, but he struck a five iron to eight feet for his fifth birdie and, after three-putting the long 13th for par, picked up further shots at the next two.
First he holed from ten feet again and then he was on in two at the par five and two-putted.
Mickelson said: "A 70 is just okay. I didn't shoot myself out of it, but I didn't make up the ground I wanted."
Woods has not won for nearly 17 months and has been working on swing changes since August.
"You have trust it now - we're in a Major Championship and it's full systems go," he said before adding that he felt he was still right in the hunt "only six back."
Lee Westwood, who had the big setback of a six on the long eighth after "over-hooking" his second, had to settle for a 72 and again was not happy with his putting.
"It's how my game is at the moment," said the World Number Two. "If you can't hole it out from four feet, you're going to struggle, aren't you?"
England's Ross Fisher shares seventh spot after a 69, along with Spain's Sergio Garcia, South Africans Charl Schwartzel and Trevor Immelman and American Brandt Snedeker.
Luke Donald, who carried the curse of winning the eve-of-tournament par three competition into the main event, returned a 72 including a birdie-eagle-birdie burst from the 14th.