The Welshman, successful at the Grand Prix in Bournemouth four months ago, next plays Ken Doherty, the 6-2 conqueror of Alain Robdioux in a much higher quality contest earlier in the day.
"I had millions of chances, I just kept missing balls all over the place," said Williams, who sprinted into a 3-0 lead in only 28 minutes. "Some of the shots I missed late in the match were so easy I'm sure my manager could of potted them."
Higgins, even more susceptible to blunders than Williams, only managed to share the next four frames by stealing two of them on the pink. Having found himself 53-0 adrift in frame eight, and staring at a 6-2 defeat, Higgins came to life with a 61 clearance to pink, but Williams retained sufficient composure to hold on in frame 10 after surging ahead with an early run of 45.
Docherty, humiliated 6-0 by Steve Davis at the corresponding stage of last year's event, took three hours and five minutes to beat Robidoux. When the 27-year-old Dubliner swiftly established a 2-0 lead with breaks of 57 and 104, Robidoux looked in deep trouble, but he battled to victory in a dour 44-minute third frame only to waste a chance to tie at 2-2.
Leading 44-0, he missed a pink and Docherty swooped with an 83 clearance to forge 3-1 ahead. From then on, Robidoux never threatened.