Grame Dott is favourite to reach an unexpected World Snooker Championships final after taking a 9-7 lead over Matthew Stevens.
The unfancied Scot built on his 5-3 overnight advantage to end the morning session of their semi-final in command, although Welshman Williams will know he still has a chance of victory.
Neither player will have been particularly happy with their performance, however, in a session that never really got going.
Williams took the early honours of the session after bringing the match back to 5-5 with the first few frames, but a century break (117) from Dott edged him back in front.
The Scot then took the next two frames as unforced errors began to dominate, before two half-century runs from Williams put him back in contention.
Dott took the last frame before the interval to put him in good stead to wrap up this best-of 33 match.
The winner will face the victor in the other semi-final between seven-time champion Stephen Hendry and world number one Ronnie O'Sullivan.
