The Englishman, in some of the most sparkling form of his career at the age of 40, posted a 16-under 194 total with one round left.
American Russell Henley shot 67 to move into second place on 12 under, as halfway leader Brian Harman (69) slipped back into a tie for third at 11 under with Anirban Lahiri of India (65) and American J.B. Holmes (65).
Casey credited his hot round to a lesson from coach Peter Kostis.
"On Thursday I had the big pulls going. Every long club in the bag was five, 10 yards left it felt like," Casey told CBS television.
"We worked hard on it yesterday after the round. Posture wasn't good enough and I was standing too far from the golf ball. He had me on the range feeling like I was going to shank everything yesterday."
The lesson paid handsome dividends as Casey picked up six birdies to go with his eagle, where he caressed a three-wood that landed in front of the green and bounced up an incline to within 25 feet of the hole.
"I was between clubs, whether to even go for the green or not," he said. "We couldn't afford to be short so we went with a three-wood, a little soft cut in there.
"That's something I rarely see, 18 greens in regulation, so clearly whatever (Kostis) told me worked."
Casey capped off his day by punching in a wedge to inside three-feet at the par-four 18th to extend his lead and set himself up for a crack at securing his second victory of the year.
James Hahn made a slam dunk hole-in-one with an eight-iron from 154 yards at the par-three 11th.
The American's ball landed with such ferocity that it took a chunk out of the edge of the hole as it clattered in.
Hahn carded 67 and trailed Casey by 10 strokes.
World number 13 Casey won the Valspar Championship in March, holding off Tiger Woods and Masters champion Patrick Reed by one stroke for his second career victory on the PGA Tour.
He also has 13 wins on the European Tour.
Casey performed solidly in the first two majors of the year, finishing in the top 16 at both the Masters and the U.S. Open.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Ed Osmond)
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