Harrison, the 2000 Sydney Olympics winner who lost a decision to Williams a year ago, floored Williams with a left uppercut.
With accurate shots, the 35-year-old left-hander opened up deep gashes on the bridge of Williams' nose and underneath his left eye.
"They don't give away Olympic gold medals. I can fight," said Harrison, who exchanged punches with Williams at Friday's weigh-in.
"In 2007 I will win the world title, in 2008 I will be undisputed. You saw today I have definitely got the skills."
"People say I've got no heart and am petrified. The bottom line is that we all have bad days at the office. Last year. I was not in the right place. I came back today with my closet cleared out. Boxing is what I want to do and let me go on in my career."
Harrison is 21-2, while Williams, who took the fight as a replacement for Matt Skelton, is 36-6.