Williams, who earlier in the week strongly hinted at retirement following the World Championship, was 9-0 up after the opening frame of the evening session, before Allen took five in a row to at last apply some pressure.
The impossible proved exactly that, however, as Williams added a 75 break to the three centuries he'd made earlier in the day, earning a meeting with Ronnie O'Sullivan.
Asked if he had been worried during Allen's rally, Williams told ITV3: "Absolutely. Nine-nil, you can’t lose really, but an hour later it’s 9-5, if he wins that one 9-6, then your bum is going, there’s no question."
The three-time world champion imposed a stranglehold on the match from the off, winning the first two frames before successive breaks of 99, 105 and 112 – he missed the final red in the latter as he closed in on a maximum – made it 5-0 as things started to turn ugly for Allen.
Williams scraped his way over the line in the sixth and eased further ahead in the seventh before completing a first-session whitewash.
He picked up where he had left off in the evening session, rattling in a clearance of 140 to go 9-0 ahead, but Allen stopped the rot with a break of 65 to avoid the whitewash.
With Williams appearing to lose concentration, Allen won the next four frames – the last of them with a break of 69 – to reduce the deficit to 9-5.
However, the Welshman regained his composure to compile a decisive 75 to make Sunday’s final, where he'll be a big underdog against O'Sullivan.
Williams said: "If I had to pick, it would definitely be O’Sullivan to play. He’s the best player by a mile, but I’m not afraid to play him. I’m going to enjoy it."
