Mickelson escaped from trouble a few times in a round of 70 that left him tied for 14th. Woods, who hasn't won this major since 2005, saw some putts absolutely refuse to fall but still had a 71, leaving him in a group in 24th place.
"I scrambled well today to stay in it," Mickelson said, "but I also let four or five good birdie opportunities slide. I'm going to have to capitalize on those opportunities [Friday] if I'm going to go low."
McIlroy and Quiros had no problems going low Thursday, doing it in different ways.
McIlroy, of Northern Ireland, the only player to go bogey-free, carded five of his seven birdies on his first 11 holes. The 28-year-old Quiros, of Spain, posted five of his eight birdies on the back nine and needed to make an 18-footer for a spectacular bogey at No. 14 after his second shot hit a branch and ricocheted to a spot near a clump of bushes.
McIlroy, who opened with a 63 in last year's British Open, said he felt refreshed after resting and working with his teacher for 10 days in West Palm Beach, Fla. For his first practice round last Friday, he played 27 holes, going around the front nine twice because he has struggled with that side in the past.
"I feel now I know the spots to miss," he said. "You can pick your targets and be aggressive. I would rather have 20 feet up the hill on these greens than six feet downhill sometimes. Because I've played the course a little bit more, you get a little bit more comfortable. That's really the only difference."
Six of McElroy's birdie putts were from 10 or fewer feet. He drained a 20-footer for birdie at the long par-3 fourth after hitting a 4-iron from 238 yards.
Quiros, playing in the last group, started his roll when his approach at the par-4 seventh hit the hole and stayed out. He slowly crept up the leader board and, after his hiccup at 14, birdied three of the last four, including a four-footer at 18 for the tie.
Quiros' score Thursday in his fifth Masters round topped his previous best by 10 strokes.
"The two previous years, I came to the Masters thinking I can shoot low, and that was my main mistake," he said. "Every single situation has to be measured - the risk, the reward. Today I was very happy making pars. That is why I probably shoot 65.
"If I push myself to shoot 65 from the first tee, I probably shoot 75, 76, like the previous years."
Quiros' impressive length played a significant part. He led the field in driving distance, averaging 309.5 yards on the two measured holes.
With conditions ideal and the hole locations relatively friendly, the 99 contestants took dead aim. The stroke average of 72.717 was less than a stroke over par.
"The back nine was very playable today, and I like that," said West Chester's Sean O'Hair, who was part of the crowd shooting 70. "I think the players like that. We don't want to play a golf course that's impossible. It's nice to make birdies, especially on the back nine. So I hope they continue to play it like this. It's quite enjoyable."
Mickelson parred all but one of his first 13 holes, including the par-5 13th, where he pushed his drive into the woods and punched out. He had to hit a low second shot under a branch at 14, and the ball rolled to eight feet from where he made birdie.
However, he knocked his second shot on 18 into the gallery and didn't get up and down, carding his only bogey of the day.
All in all, it was a good day for McIlroy, who bought a football earlier this week and wants to learn how to throw it better. But while practicing his throw in the street with friends, a woman living near the home where he is staying asked him to keep the noise down.
"I just said, 'Sorry, we'll go inside now,' " he said.
Was he running any pass patterns?
"I don't even know what that means," he said.
Contact staff writer Joe Juliano at 215-854-4494 or firstname.lastname@example.org.