England's former world No.1 Rose carded a one-under-par 71 on Friday to cling to the 36-hole lead at eight under, holing a clutch par putt on the last with his rivals circling.
America's Bryson DeChambeau chipped in from a bunker on the way to a four-under 68, stalking Rose a shot back in outright second.
Canada's Corey Conners was a stroke further back and will partner McIlroy (six under) on Saturday after the Northern Irishman's emphatic response to a Thursday meltdown that had seemingly blown his chances of a maiden green jacket and career grand slam 11 years in the waiting.
Defending champion Scottie Scheffler remains in the mix at five under while Tyrrell Hatton dropped two late shots to be equal with the world No.1.
Day quickly emerged as Australia's main hope, skipping onto the front page of the leaderboard with three front-nine birdies to reach five under and sit in a tie for fifth through 13 holes.
He narrowly missed two more birdie putts around Amen Corner and left two more short down the stretch, a bogey at the last ensuring Ed Sneed was the last man to go bogey-free through the first 36 holes in 1979.
Min Woo Lee bounced back from a double bogey on the first to card an even-par 72 and be one under, just outside the top 20.
But the wheels fell off for Cameron Smith (five over, 71, 78), who started the day at one under before going backwards.
He missed the cut for the first time in nine visits while Adam Scott (five over, 77, 72) also has a free weekend for the first time in 16 years.
Cam Davis (nine under, 74, 79) finished close to last to make it five consecutive missed cuts this season.
But all eyes are on world No.2 McIlroy, who wilted on Thursday with a duo of double bogeys after he had soared to four under to seemingly kiss his chances of a maiden green jacket - and career grand slam - goodbye.
The Northern Irishman put that behind him on Friday, making back-to-back birdies after the turn and an eagle on the par-five 13th that shot him back into the guts of the leaderboard.
He then launched an audacious approach from the pine needles, over the towering trees, on the next hole that led to a tap-in par.
McIlroy edged a shot closer to the leaders with a birdie on the 15th - the par-5 he took seven on a day earlier - to finish just two shots off the pace.
"I'm just really proud of myself with how I responded after the finish last night," McIlroy, who won his fourth and most-recent major in 2014, said.
"I just had to remind myself I played really good golf yesterday and was not going to let two bad holes dictate the narrative for the rest of the week.
"Once I left the property I tried to leave what had happened here.
"I rushed home to see (daughter) Poppy before she went to bed.
"I had a good conversation with Bob Rotella (sports psychologist) about not pushing too hard too early, just tried to stay really, really patient and that was rewarded with a nice little stretch in the middle of the round.
"I don't think I proved anything, if anything just backed up the belief I have in myself and the belief that I'm as resilient as anyone else out here."
Phoenix native Matt McCarty (five-under) double-bogeyed the first hole and dropped another shot on the next, but still carded a four-under 68 to take a brief clubhouse lead.
The historic recovery included eight birdies in 12 holes, McCarty the first to shoot 68 or better in a round in which he was three-over or worse at any stage.
Five-time major champion Brooks Koepka could afford to drop a shot on the last to make the cut but had a quadruple bogey, while 67-year-old Bernard Langer's 10-foot putt to make the cut just missed in what was his last appearance.
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