The nine-year-old was bouncing back from successive falls in Wincanton’s Somerset National and then the Eider Chase at Newcastle to prevail this time by three lengths at 20-1 from Ms Parfois.
James Bowen always had Potters Corner close up, going well behind a steady pace set initially by Bryony Frost on Milansbar.
Ms Parfois, a Grand National entry for resurgent Anthony Honeyball, was also prominent throughout and led into the straight in driving rain and a fierce gale on increasingly heavy ground.
But it was Potters Corner, in strong contention when coming down on his previous two starts, who got it right and kept going the best over this marathon four-and-a-quarter-mile trip.
There were 12 more lengths back to Get On The Yager in third, with Prime Venture fourth another three away.
Williams, trains Potters Corner for a syndicate involving Wales rugby union international Jonathan Davies.
Williams said: “It’s great – he was a bit unlucky in the Eider Chase and the Somerset National.
“He’s pulled his jumping together. We’ve worked hard on it in the last fortnight, (and) it’s all come together now.”
“When he was still bang there, I thought it would be great if he finished second - so I’m delighted he won.”
Trainer Caroline Bailey is hoping Reckless Behavior will be on his best behaviour at Southwell on Monday - after getting loose and finding himself on the streets of Uttoxeter on Saturday.
The seven-year-old unshipped rider Sean Bowen at the start of the H Brown & Son Recycling Handicap Chase on Midlands National day, and went on to crash through the rails and exit the racecourse.
Bailey said on Sunday: “I’m not sure how he actually got out of the racecourse, but I gather he lobbed over a few roundabouts and ended up outside a pub. I’m sure the people inside must have thought they were seeing things after watching the rugby.
“A lady followed him out of the racecourse and I gather she was the one who caught him, but I’m not sure.
“I’m told a few people came out of the pub to see what was going on, which you would do if you saw a horse with a saddle and a number cloth on him outside!”
She added: “He’s actually not a nasty horse at all - he’s just very sharp.
“I think it’s a nerves thing as much as anything. We’d freshened him up since his last run and sometimes he doesn’t channel his quick mind in the right direction.
“The vet inspected him afterwards and he was absolutely fine. We cantered him this morning and everything was good, so we’re trying again at Southwell tomorrow.”
“He needs soft ground, so we have to run him and if he behaves himself I hope he’ll run well.”