Masters champion Watson used his astonishing power to compile five early birdies on his way to a three-under-par 69 in ideal conditions at Muirfield Village.
He posted a 12-under 204 total, one stroke ahead of compatriot Scott Langley (67) with one round left.
Young Japanese player Hideki Matsuyama (69) was two strokes behind, while world number one Adam Scott of Australia (68) trailed by three despite a bogey at the final hole.
Casey, who started the day with a three-shot lead, had a nightmare round, struggling with almost every facet of his game in a 76.
The former world number three has recently shown glimpses of his old brilliance as he seeks to regain his full playing status on the PGA Tour, but has been unable to string together four good rounds.
Watson, aiming to become the first left-hander to win this prestigious Jack Nicklaus-hosted event, played far more adventurously than his words suggested.
"I just kept my head down, grinding away," he told CBS television.
"Shooting in the 60s every day is my goal. It's working out so far."
Watson made his move with five birdies in the first seven holes, charging to the turn in four-under.
He was not as precise on the back nine, coming home in one-over, including a bogey at the par-four 18th, where he sprayed his second shot right of the green.
The 22-year-old Matsuyama, meanwhile, was in contention for the second successive week after sharing the lead going into the final round at the Colonial, where he tied for 10th behind winner Scott.
Scott continued to justify his ranking as world number one with another impressive round that included a 25-foot eagle at the par-five 15th.
"It's feeling good this week, better than last week," he said ominously.
"I was finding my feet again last week and took a lot of confidence out of winning and came here swinging the club very nice."
Second-placed Langley, in his second year on tour, may not be a household name but a third-place finish at the Tampa Bay event in March showed his promise.
Earlier Saturday, a large and generally supportive gallery watched Phil Mickelson shoot 72, barely 12 hours after media reports that he was under investigation by the U.S. Federal Bureau of Investigation and the Securities and Exchange Commission for possible insider trading.
Mickelson, who told reporters he had done nothing wrong and was cooperating with authorities, finished the round at two under par, 10 shots behind Watson.
- Sports & Recreation
- Scott Langley
- Hideki Matsuyama