Higgins and Xiao were pressed for time to complete their match before the afternoon session, but were taken off the table with the Scot 12-11 ahead.
They resumed in the morning with the score level at 8-8 and exchanged lengthy frames, which eventually left Higgins one frame from victory.
However, he squandered a chance to seal it and allowed Xiao to swoop in and send the match into a deciding frame.
But Higgins – a four-time winner at the Crucible – shook that disappointment off with a 75 break to finally ward off Xiao after 10 gruelling hours.
"What a weird feeling that was, getting home when you know you're coming back for only one or two frames, it's just a surreal feeling," Higgins told the BBC afterwards.
"I thoroughly enjoyed the game, I really did, because it's just an unbelievable venue to play in.
"You're playing good some minutes, the pressure is on you, the crowd are all getting involved. You can't replicate playing here."
Higgins' next opponent Williams booked his spot in the quarter-finals after seeing off Iran's Hossein Vafaei 13-10 earlier on Saturday.
Welshman Williams resumed up 9-7 and took two of the first three frames to keep up his momentum in the clash.
Vafaei closed the deficit to 11-10, which did not prove to be significant as Williams cleaned up and finished with a 115 break.
Meanwhile, Ronnie O'Sullivan crafted a 6-2 lead against Pang Junxu in the first session of their second-round match.
Seven-time champion O'Sullivan capitalised on a glut of errors from China's Pang, claiming each of the first four frames at the Crucible.
Pang got himself off the mark with a handy 119 break before O'Sullivan eventually took back his four-frame advantage heading into the resumption on Sunday.
Luca Brecel also put in a scintillating display to open up a commanding 7-1 advantage over Ding Junhui.
After dropping the first frame, the Belgian turned on the afterburners to reel off seven straight, before departing the arena to a standing ovation.
England's Ben Woollaston trails Si Jiahui 5-3 and Zhao Xintong leads Lei Peifan 10-6 in an all-Chinese affair.