He recorded a 17-under 193 total, while Northern Irishman McIlroy (63) vaulted into equal second place with American Schauffele (67) on 16-under.
McIlroy sank a 40-foot birdie putt at the last, while Schauffele bogeyed the same hole, missing a 10-footer.
Englishman Tommy Fleetwood (62) and American Rickie Fowler (65) were two behind the leader.
Tiger Woods did not capitalise on a birdie, birdie start, plodding to a 66 that left him five shots adrift.
Preferred lies were allowed after heavy overnight rain left puddles on the waterlogged fairways. With marshmallow-soft greens and little wind, the course was at the mercy of the field.
Despite his lead, Rose was not totally satisfied with his performance on the course where he won the 2010 AT&T National on the PGA Tour.
"Today was a struggle at times," he told Golf Channel. "Not every shot felt in complete control.
"I didn't drive it as well as yesterday, especially on the back nine, wasn't able to make a birdie but more importantly was able to make a couple of good par saves, especially 17, and kept my nose ahead of the field.
"I'm doing a lot of things well. All aspects of my game are turning up for me most days. It can never be perfect every day."
Rose also won the 2013 in suburban Philadelphia at nearby Merion.
McIlroy bounced back from a double-bogey at the par-three eighth with an eight-foot eagle at the par-five ninth.
"Weird day," he said. "They put a lot of the tees up. It was very wet but if you didn't shoot 65 you were losing ground. It was one of those days you had to stay aggressive."
His birdie at the last brought a smile to his face.
"It was going a little bit firm. It was nice to see it go in."
Halfway leader Schauffele battled his driver but the rest of his game was solid.
"I guess I hung in there," he said. "I'm just happy to have a shot tomorrow."
The event is the third of four playoff events on the PGA Tour.
The top 30 players on a season-long points list after Sunday's final round will advance to the Tour Championship.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Peter Rutherford)
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