The veteran cuemen, who between then have won seven world titles, resumed on Wednesday all square at 8-8 in the best of 25-frames quarter-final at the Crucible Theatre in Sheffield.
Wales star Williams then moved to the brink of victory by winning the day’s opening four frames to go 12-8 ahead.
But four-time champion Higgins ensured the match would go to a deciding frame after the Scotsman reeled off breaks of 94, 114 and 67.
Yet it was Williams who prevailed after Higgins missed a tense blue on the top cushion to seal a 13-12 victory.
“There was not one bit of nerves,” Williams, 50, insisted afterwards. “I don’t really get it. I’ve only had nerves a handful of times in my career.”
He added: “I wasn’t thinking he (Higgins) would miss it. From 12-8 to 12-all I had not done much wrong and I was thinking, ‘what can I do?’
“It’s just a pleasure playing now. We got the standing ovation walking in and everyone was cheering. You have to enjoy it because you don’t know how many times you’ll be coming back here.” (AFP)
