Williams took down Cross 3-1 at Alexandra Palace on Monday night, as the world number five became the 14th seed to fall in the second round.
Cross took a tense opening set and looked to be racing away with the second before Williams recovered from two legs down to level.
It ignited something within 'Shaggy', who capitalised on some wayward Cross finishing to gain revenge for his loss to the 2018 champion two years ago.
"It's so tough because Rob is one of my closest friends," said Williams, who reached the semi-finals of last year's World Championship.
"Neither of us were great tonight, but Rob missed doubles and gave me a chance, so when you get given opportunities, you've got to take it.
"I'm always confident, regardless of who I'm playing, but I'm just looking forward to having Christmas with the family now."
Williams returns to the London stage after Christmas to face Ricardo Pietreczko in the third round.
German Pietreczko beat former world youth champion Gian van Veen earlier on Monday.