Former jockey Williams had saddled the first two home in the Coral Trophy at Kempton in February and on the same afternoon Win My Wings won the Eider Chase at Newcastle.
He probably never thought he would equal that achievement - but in saddling the first two home in Scotland's biggest race, the Welsh handler once again proved there are not many better when it comes to training staying chasers.
Win My Wings - the 13-2 joint-favourite with Kitty's Light - was ridden with extreme confidence by Irish amateur Rob James, whose 7lb claim offset almost all the 8lb rise she incurred for winning at Newcastle.
James had only ever ridden one other winner in the UK, Milan Native in the Kim Muir at the Cheltenham Festival, but is one of the most prolific winning point-to-point jockeys in Ireland.
Having settled his mare in mid-division behind a generous early pace, he kept out of trouble on the outside before joining Ask A Honey Bee a long way from home.
Stamina is the winner's forte and as the likes of Major Dundee and Ashtown Lad began to tire, Win My Wings just pulled further and further clear.
James allowed her to coast home after the last, as Kitty's Light stayed on dourly to claim second, seven lengths adrift. Major Dundee was third with Fidux fourth.
Williams said: "I feel sorry for Kitty's but nothing would have beaten her today, that's how it looked to me. It was some performance.
"I was pretty confident the whole race to be honest, but I was just a little worried if she'd done a bit too much too early in the race.
"Rob kept her out of trouble on the outside and she jumped great.
"I don't know about Aintree next year. She wouldn't be over-big which would be a concern and the thing about Aintree is you have to build your whole season around it and there's a lot of fun to be had before then. I'll talk to the owners.
"She's been to France before and won so that style of racing does suit her, but I don't think she'll go this year as she's had two hard races.
"She might go to Sandown for the bet365 Gold Cup, she does have that option so I wouldn't have thought it would be France this year. The thing is with these mares when they get on a roll you want to keep the ball rolling. We'll sit down after the weekend and chat sensibly.
"Sandown is an option for Kitty's as well. He's had some hard races and while he hasn't won a big one this season he's won plenty of prize-money.
"He's got time on his side still, he's still only six and he'll win a big one some day, he's got plenty of time."
He added: "They are two wonderful horses, two great jockeys and it's just a shame all the staff couldn't be here to celebrate, so we'll do that when we get home."