Welshman Ray Reardon won his sixth world title in 1978 at the age of 45 to become the oldest victor of the event.
But four-times world champion Higgins has won five straight frames to level the final at 15-15 in the race to 18.
And his promise to bare all for his winning press conference turned out to be the naked truth as he spoke to the world's media dressed in nothing but a towel.
Williams, who failed to even qualify for last year's World Championship, said of his family: 'I'm sure they've enjoyed it.
And wife Jo and kids Connor, Kian and Joel were all left a little red-faced by his celebration antics.
Before the start of this season, Williams had not won a ranking event since 2011.
Asked how his success felt, Williams said: It feels a little bit uncomfortable at the minute.
He also charmed spectators a few frames into the contest by having a bag of minstrels handed to him by a fan in the audience, as well as a few wine gums.
Mark Williams, 2018 world snooker champion, was an outsider.
Williams arrived naked apart from a sponsors towel sparing his blushes - under orders from supremo Barry Hearn - but soon took it off after sitting down.
Speaking to the BBC after last night's win in Sheffield, Williams said: "It's unbelievable". Twelve months ago I was thinking about chucking it, and here I am doing an interview having won the 2018 World Championship, naked.
"I don't think she wanted me in the house 24 hours a day".
"To best honest, if I won this next year, I'd do it again".
'I don't know where that last break came from but it's one of the best I've made under pressure in my life.
"I wasn't giving in easily, and even when Mark was closing me out at 14-7, I wasn't really getting clear-cut chances and missing easy chances", he added. I didn't want to lose with a session to spare, and at 14-7 that looked possible.
Another trademark clearance from Higgins, 82 from 47-0 down, got him within two frames.
The players resumed yesterday with Williams 10-7 up and most expecting an immediate Higgins fightback.
Back came Williams, and a century break to go one frame away from victory suggested his nerves had settled.
A missed pink in the next frame allowed Higgins back into the game and made it 17-16.