Both players made just two breaks over 50 in a scrappy contest, but Welsh veteran Williams used all his experience to edge three frames on the black, one on the pick and one on the blue.
Williams will face Mark Allen in the last four after the Northern Irishman recovered from 6-3 and 8-7 down to beat China’s Ding Junhui 10-8.
Allen, who made the highest break of the tournament to date with 142 in frame 10 to spark his comeback, won the 16th frame on a re-spotted black and secured victory in style with a 127 clearance.
Allen, who trailed 5-3 after the first session, told ITV4: “I played better tonight, still relied on a few misses from Ding but played better on what was a really, really tough table. It was not a lot of fun to play on.
“I don’t want to make excuses for us both but the table was tough and my action started to go because you were having to hit the ball so hard.
“It was very, very heavy and the pockets played very tight, whereas table one looked like it was playing beautifully.”
Earlier in the day, Gary Wilson came from 8-7 down to beat Zhang Anda 10-8 and book a semi-final showdown with Ronnie O’Sullivan, a player he beat en route to winning the 2022 Scottish Open.
“I’m not someone who crumbles because of who I am playing,” said Wilson, who remains unhappy with his technique despite reaching the last four.
“For me, it’s all about how I am feeling and playing. If my action is gone then my confidence is on the floor and I can’t find any way of hitting it.
“If that happens then it doesn’t matter who I’m playing. I am trying to iron that out, it’s not really working. But I am in the semis so let’s see what happens.”
