Williams’ 10-7 win over qualifier Martin Gould was overshadowed by an incident prior to the match in which the 44-year-old claimed his 12-year-old son Kian was prevented from visiting him in his dressing room.
The Welshman’s allegations, which the governing body rigorously denied, are the latest in a series of gripes he has with the organisation over perceived unfair treatment during his reign as champion.
Williams said: “They (World Snooker) have obviously got some kind of beef with me, but whatever it is you’ll have to ask them.
“I’ve been having all this nonsense all season really and this morning was the last straw really. My boy tried to get in to say good luck and I couldn’t get him in because I’d used my two passes.
“It’s pathetic in my eyes. If you’re the world champion you expect some kind of [favour]. But I wasn’t going to let it play on mind. It’s only my opinion and they will say that nothing’s wrong.”
A spokesman for World Snooker denied that Williams’ son had been denied entry to the dressing room, but pointed out that the player had chosen to give his two allotted passes to his coach and his friend.
The spokesman said: “Every player in the event is allocated two backstage passes. And they can make their own decisions who to give those to. At no point were his children refused entry.”
Williams, who now goes on to play either David Gilbert or Joe Perry in round two, had already expressed his displeasure with tournament organisers over what he considered to be a lack of sufficient profile in its promotional materials.
And on the eve of the event he had claimed World Snooker officials would prefer anyone but him to win the title this year, an accusation the governing body also vehemently denied.
The lingering bad feeling appeared to have done little to affect Williams’s game as he won five frames in a row to establish a 6-3 lead at the end of the opening session.
Williams moved within one frame of victory at 9-4 after resuming in the evening but a belated rally from Gould, with consecutive breaks of 70 and 87 and 76, brought him back to within two frames.
A superb long red in the next finally paved the way for Williams to get over the line and his vanquished opponent said he would not be too surprised to see the Welshman go on to win a fourth title.
Referring to Williams’ much-publicised build-up to the tournament, Gould quipped: “As long as he stays off the booze, the kebabs and the Minstrels I think he’ll be all right.”
Neil Robertson will return on Sunday evening one frame away from only the second whitewash in Crucible history after establishing a 9-0 lead over Michael Georgiou.
The Australian fired two centuries to overwhelm Georgiou, who faces the prospect of being the first player to exit without winning a frame since Eddie Charlton was beaten 10-0 by John Parrott in the 1992 first round.
Ding Junhui holds a 6-3 overnight lead over Anthony McGill and Luca Brecel is edging Gary Wilson 5-4 with both matches due to play to a finish on Sunday.