The 46-year-old was in impressive form to knock out four-time Crucible champion John Higgins 13-7, and claim a quarter-final spot in Sheffield.
It evoked memories of 2018, when the Welshman beat Higgins 18-16 in a titanic final.
But Williams is not getting carried away, ahead of his quarter-final match against either Mark Selby or Mark Allen.
“I think I played really good solid stuff the whole way through,” said Williams. “I can’t play much more solidly than that.
“My safety was good and some of my long balls were good. Some of the ones I went for were ridiculous. I loved every minute and I was enjoying it.
“If I get on a roll, I can win a few frames in half an hour. It can put a bit of pressure on their safety more than anything.
“If their safety isn’t any good, I’m going for it regardless of where the balls are.
“I probably played as well tonight as I did back in 2018. I’m just being honest though.
“Back in 2018, I thought I had a great chance of winning this and told people that before we even started. I don’t feel like that this year.
“If I felt like that I would tell you, whether or not you believe me, I don’t know.”
If the 46-year-old reaches the last four he would be the oldest Crucible semi-finalist since Ray Reardon achieved the feat in 1985, aged 52.
Williams is joined in the quarter-finals by Neil Robertson after he beat Jack Lisowski.
The Australian, leading 9-7 overnight, produced breaks of 126, 87 and 70 as he wrapped up a 13-9 second round victory.
Robertson has only reached the semi-finals once since winning his only world title in 2010 - but he has looked in good form in Sheffield this year, and said he has carried forward his momentum from a successful Tour Championship
“The Tour Championship was certainly the best I’ve ever performed in an event, certainly from start to finish,” he said.
“I’ve kept that momentum going into the first two rounds here, but the form and results don’t really matter - it’s all about what I do in my next match.
“I’ve got to forget about playing well or anything and just prepare as well as I have done.”
On the match itself, the 39-year-old said: “Yesterday was an awesome session of snooker, I think we both had four frame-winning visits each in the eight frames and so coming into tonight (this morning) I felt really good.
“I thought he had thrown just about everything at me that he could possibly throw at me and then today I kept that going again, had a little bit of luck today...which was nice.
“But I ended up making it count with frame-winning visits, which is really important. But Jack did really well throughout the whole match.
“Usually he loses his focus in the longer distance matches but throughout the whole match his safety was very good and he made me work really hard for my chances.
“He’s a player that, out of all the other players, I really want to see do well.
“He’s such a nice guy and so talented, so this will be good for him, moving forwards.
“I think if he was playing someone who probably wasn’t playing as well as I was, he probably would have won the match, so I feel very good because that was a really really good test.”
Tickets for the concluding session of the Betfred World Championship final at the Crucible Theatre have virtually sold out as Sheffield stages a successful return of fans to indoor sporting events.
Under the Government-led Events Research Programme, the World Championship is the first indoor sporting event in the UK to welcome back fans in 2021.
The potential capacity started at 33 per cent for the first round and rises to 100 per cent for the final on May 2nd and 3rd.
Tickets for the afternoon and evening sessions on Sunday May 2nd are still available, as well as the afternoon session on Monday May 3.
A WST spokesman said: “It has been a fantastic event so far and amazing to see fans returning to live sport.
“Usually tickets sell out a year in advance so this is a unique opportunity to be there and experience the extraordinary atmosphere.
“To have a full house for the final night will be a historic occasion and we are proud to be part of the Events Research Programme which will help the whole country move forward through scientific data.”
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