Higgins won five straight frames to progress having watched fellow multiple world champion Williams win the first two frames, including a run of 64 in the first frame.
Higgins rolled in 87 in the third frame and the tournament's highest break so far of 144 in the fifth frame.
“There was very little in the match, just a bit of luck and that was the reason I won,” said Higgins, who will meet Ali Carter in the quarter-finals after the former double World Championship runner-up enjoyed a 5-4 win over Daniel Wells that included a 130 knock in the seventh frame.
Selby eases through in early World Open test as Williams thumps Stevens
“He’s one of the best players I have ever played and I have the utmost respect for him.”
Thepchaiya Un-Nooh was a 5-0 winner against World Championship semi-finalist Alan McManus in just under an hour.
He will meet another Scot Anthony McGill in the quarter-finals after McGill ousted Matthew Selt with a 5-2 success.
John Higgins makes highest break of tournament
Defending champion Shaun Murphy enjoyed a 5-1 win over Kurt Maflin. He will meet Joe Perry in the last eight after the 'Gentleman' edged Ben Woollaston 5-4.
"I’m a professional snooker player and I try my hardest every time. I always prepare to my best,” said Murphy.
“I think all of the players owe it to the fans to be as ready as possible.”
Murphy completes victory with lovely century
Latest results from World Open last 16
Joe Perry (Eng) 5-4 Ben Woollaston (Eng)
Shaun Murphy (Eng) 5-1 Kurt Maflin (Nor)
Neil Robertson (Aus) 5-1 Ryan Day (Wal)
David Gilbert (Eng) 5-0 Zhang Anda (Chn)
Allister Carter (Eng) 5-4 Daniel Wells (Wal)
Mark Williams (Wal) 2-5 John Higgins (Sco)
Anthony McGill (Sco) 5-2 Matthew Selt (Eng)
Alan McManus (Sco) 0-5 Thepchaiya Un-Nooh (Tha)
Carter whitewashes Higgins to reach World Open semi-finals
World champion Selby loses to Thepchaiya at World Open