Schauffele held a three-shot advantage at day's end after world No.2 Rory McIlroy, a three-time winner of the tournament, finished an up-and-down round with a bogey at the 18th hole.
McIlroy settled for a four-under 67 to be tied for second with Collin Morikawa and Sweden's Alex Noren.
Day posted a 68 to sit in a seven-way share of fifth after opening eagle-birdie to be three under through two holes.
Two bogeys offset two more birdies but Day still finished as the leading Australian, two strokes ahead of Cam Davis.
Schauffele started on the back nine at Quail Hollow Club and birdied five of his first eight holes before making his only bogey of the day at No.18.
After a quiet start to the front nine, he threw a dart on his second shot at the par-5 seventh hole, his ball glancing the side of the cup for a would-be albatross before leaving him just five feet for eagle to get to six under.
Schauffele's drive at No. 8 flew far right, but he managed to find his ball and was allowed to move non-embedded rocks out of his path before hitting his second shot onto the green. He followed that critical par save with a six-foot birdie putt to end his day with a flourish.
McIlroy's highlight was a perfectly struck 50-foot eagle putt at No.7 that gave him the solo lead at the time at five under. The rest of his day was a series of bogeys and bounce-back birdies until he failed to save par from seven feet at No.18.
Justin Thomas, Russell Henley, Taylor Moore, Lee Hodges, South Korea's Sungjae Im, Austrian Sepp Straka were also three under with Day.
The 69-man field is playing four rounds without a cut at the sixth signature event of the season, which doubles as a tune-up for next week's PGA Championship.
