The 38-year-old Englishman nabbed six birdies over the opening nine holes and parred through the inward nine to stand on 17-under par 193 after 54 holes at rainy Aronimink Golf Club.
American Xander Schauffele, who led after a second-round 64, was level with Rose until a closing bogey to finish a round of 67 to stand on 194 with four-time major champion Rory McIlroy of Northern Ireland.
"A one-shot lead doesn't really mean much and it doesn't change my approach tomorrow as I just have to play better than the guys around me," Rose said.
Fourth-ranked Rose would move to world number one for the first time in his career with a victory unless either top-ranked Dustin Johnson or second-ranked Brooks Koepka, who share 33rd after three rounds, have a two-way share of second.
Rose would become the third English man to reach the ranking summit after Nick Faldo, Lee Westwood and Luke Donald.
Bahamas-based Briton Rose is no stranger to winning in Philadelphia, having capturing the 2010 PGA National, and the second of his nine PGA titles, on this week's host layout.
In 2013, Rose captured his first major title at the US Open at nearby Merion.
Rose ran off four consecutive birdies, a spurt ending at the par-3 fifth and topped by an 18-foot birdie putt at the third. He also birided the par-3 eighth from 12 feet and the par-5 ninth from three feet.
"It was a good day for me today and while it was a day I felt I didn't play that well, it was a good day for scoring and I made my score on the front nine," Rose said.
"I know there will be guys behind me on the leaderboard who will be gunning to play well and there will be guys who will just play well."
Schauffele, 24, lipped out a nine-foot par putt at 18 to stumble back alongside McIlroy, who brilliantly regrouped after a "no frills" Friday 69 to grab a ninth-hole eagle and seven birdies in his score of 63.
McIlroy's only hiccup was again making a mess, for a third day running, of the eighth, taking a double-bogey after two earlier bogeys.
"I had missed a couple of shots ones on Friday but today I made the putts I needed to while I also hit more fairways that gave myself more opportunities," McIlroy said.
"But then it was a weird day as they put a lot of the tees forward and while the course was very wet from all the rain we had last night, if you didn't shoot 65 you were losing ground.
"It was just one of those days you had to stay aggressive."
Sharing fourth on 195 was England's Tommy Fleetwood and American Rickie Fowler. Fleetwood posted his second 62 in a row with eight birdies.
"If I had to choose which was the better 62 I would take Friday's as I just seem to hit the ball marginally better," Fleetwood said. "But then who's going to complain when you shoot a 62?"
Tiger Woods produced his best start in the three days with back-to-back birdies, then birdied the 14th and par-5 16th on his way to a 66 that left him sharing 11th on 198.
"Today was one of those days where it was really frustrating because I hit the ball well enough to shoot a low score," Woods said.
"I'm now going to have to shoot one of those 61s or 62s just to have a chance. The golf course is soft and everyone is making birdies. You can be aggressive. I got to take a run at it."
Officials moved Sunday tee times early to try and finish ahead of predicted Sunday afternoon thunderstorms. Players will be in threesomes off the first and 10th tees to try and avoid a Monday finish.