But the former British heavyweight champion showed remarkable resilience and strength to stop the American inside four sensational rounds.
His promoter, Frank Warren, said: "Danny grabbed lightning in a jar when he knocked out Mike Tyson and took heavyweight boxing by storm. Now he has the chance to do it again.
"Danny has been a Cinderella man but now here he is, challenging for the prestigious WBC heavyweight title. Believe me, on the night I think there could be another upset."
Williams, himself, believes he could be just nine minutes - the equivalent of three rounds of hard boxing - from realising his dream of becoming world champion.
The 31-year-old from Brixton knows that, just as with Tyson, he will have to weather an early storm if he is to cut the 6ft 7ins Klitschko down to size.
Williams, who had a height advantage over Tyson but who will be giving away six inches to the champion, said: "As in the Tyson fight the first three rounds will be the most dangerous for me. I've got to get inside those long arms.
"Klitschko is good, but slow and robotic with suspect stamina. And he gets tagged as we saw against Lennox Lewis and Corrie Sanders."
Klitschko lost to Lewis in June last year when he suffered severe cuts to his left eye.
When Lewis subsequently announced his retirement from the ring, Klitschko and Sanders fought for the vacant WBC title in April.
It was a cracking brawl with southpaw Sanders nearly scoring a win in the first round when he caught his stiff opponent with a booming left. But Williams will have taken note of the way Klitschko came back to send 38-year-old Sanders into retirement with an eight-round stoppage.
Williams said: "I'm going to be fighting probably the best heavyweight in the world but come 11 December I'll be bringing the world title back to Britain. Trust me."
