American leader Kevin Kisner was in the clubhouse on eight-under par 134 for 36 holes after his second consecutive four-under 67 but Day and Matsuyama were the first players to make a charge at him in the year's last major tournament.
His real danger will be Matsuyama, who looms as the first golfer from Japan to win a major.
Grayson Murray is at 210 after shooting 69.
Patrick Reed, Gary Woodland, Scott Brown and Francesco Molinari are also at 2 under.
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Rickie Fowler, still trying to get his first major, had a one-under 70 and is at three-under 139.
Day nearly landed a rare albatross on the par-five seventh hole and the resultant kick-in eagle kickstarted a run of five birdies in the next seven holes - either side of a weather delay - to enable a five-under-par round of 66 to race to six under in total. He finds himself tied with Kisner for the lead.
"I kind of accept the fact that I'm essentially out of this tournament pending some form of insane stuff the next couple of days", Spieth said. "Now I'm in a dogfight Sunday, and I have to be prepared for that".
He doubled the 12th, bogeyed 13th, birdied three in a row from 14th to 16th and then bogeyed 17th and messed up with a quadruple bogey, raising questions over his shot selection. He's the hardest worker out here right now just because he wants to win. If he didn't make those birdies, he anxious he might have shot himself out of the tournament. "Now I'm in a dogfight (today), and I have to be prepared for that".
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The ball lipped the cup for an albatross. He managed to two-putt and retain the lead.
Mickelson, 47, had played well at Quail Hollow when the Wells Fargo tournament was played here. I probably didn't quite hit it as well off the tee as I did yesterday and wasn't putting myself in positions where I could go at a lot of pins.
"I didn't make the putts I've been making the first two days and had just a awful finish there", said Kisner. "That was a stupid play ... but that puts a little fire in me for tomorrow". He has been playing as well as anyone lately and it showed on Friday. "Even just that - so yeah, it's a much tougher practice, and I'm not - after what I've witnessed over the past two days, no, I'm not surprised to see so many guys be over par".
Like Matsuyama, Stroud is happy to be in the hunt. The PGA Championship victor at Whistling Straits two years ago shot a 66 and was two shots behind. "You know, I've been waiting on this a long time".
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