World number three Williams led 11-5 overnight and needed less than an hour to seal his place in the last four.
He will now play the winner of the contest between Ronnie O'Sullivan and John Higgins for a place in the final.
Ding Junhui leads Mark Selby 10-6 after a tense and attritional session of their quarter-final contest.
The last frame of the session, eventually won by Ding, included a period of more than 40 minutes without a ball being potted.
It was a long, drawn-out frame, with Ding building a 47-0 advantage before Selby tried to claw his way back to ensure he went into the interval only two frames behind.
However, after both players missed a series of presentable openings, Ding eventually closed out to take a four-frame advantage.
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It's been a long time, eight years - it'll be nice
Mark Williams on reaching the last four
Ding had gone into Wednesday morning's session leading 5-3 and quickly underlined his intent with a break of 121.
It looked as though Selby might fall 7-3 behind when Ding struck a break of 50 in the following frame but the Leicester player battled back to reduce the deficit.
A series of drawn-out frames followed and the session did not finish until after 1400 BST.
That match will play to a finish on Wednesday evening, with the winner taking on either Judd Trump or Graeme Dott for a place in the final.
Welshman Williams won the world title in 2000 and 2003 but until this year had reached the quarter-final stage only once since his last victory at the Crucible.
"It's been a long time, eight years. It'll be nice," said Williams of his forthcoming semi-final appearance. "Once it goes down to one table it's totally different.
"You've got loads of room and that's when it becomes a real venue. I haven't been there for so long, I'm looking forward to it."
Northern Ireland cueman Allen left a red hanging over the pocket in the opening frame of Wednesday's session and was punished as Williams fired a break of 61.
When Allen missed a sitter of a red at 39-17 ahead in the next, Williams produced a match-clinching clearance of 65.
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Behind the scenes at the Crucible with Rob Walker
Allen was left to rue a series of missed opportunities as Williams opened up a 5-3 lead during the opening session.
"I played probably the best snooker I've played in the tournament and managed to somehow throw three frames away. I made 59, 60 and 66 and lost all three frames," 25-year-old Allen reflected.
"I should have been 6-2 in front but somehow I came out 5-3 down, but that's what Mark does best. He knows how to win and he knows how to get the most out of a session which is something I'm still learning to do.
"From then on it was a bit of a struggle to hang on to his coattail and he showed what a class player he was by pulling away so easily."
Williams agreed that the opening session had been crucial and added: "How I managed to be 5-3 up I'll never know.
"He was knocking in 50s and 60s for fun really, and I kept clearing up and nicking them.
"It probably hurt him a little bit early on and I dominated the match from thereon."
Source link: http://news.bbc.co.uk/sport2/hi/snooker/13209141.stm
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