In the midst of the dramatic climax at the Millennium Stadium, hot-shot Williams' last-gasp try also took him past Rory Underwood to become the best Test finisher in the northern hemisphere.
Next up for Wales is a historic Friday night showdown with France in Cardiff. Now birthday boy Williams wants to celebrate in style by re-writing his name in the history books and ending Edwards' 32-year-old record.
Williams, who turns 33 on Friday, said: "I love scoring tries and that's the main reason why I'm in the squad. It will be a massive honour to beat Gareth Edwards' championship record.
"It would be great because he is a legend of the game. In fact I'm a friend of his now - it's absolutely crazy.I have enjoyed scoring tries ever since I was a kid and I am football's equivalent of a striker.
"It is what I am here to do and I'm sure Warren Gatland and the coaches want me to keep going. Maybe I'm greedy but I try to pop up everywhere and then reap the rewards by being on the end of that final pass.
"But I try not to think too much about the records. Of course, I want to continue and score more tries for Wales and eventually get up to the likes of David Campese."
Wales' record try-scorer lies 13 scores behind the former Australian star after his 49 touchdowns for Wales and brace for the British Lions.
The Ospreys ace has scored an incredible 20 tries in his last 23 appearances for Wales with a remarkable strike-rate (87 per cent) which is even superior to Chelsea star Didier Drogba who has netted 19 times in 22 Premier League games this season (86 per cent).
Now seventies great Edwards believes Williams' red-hot form will inspire Wales to victory and break his own record against Les Bleus.
Edwards said: "Shane is a world class player and I couldn't think of a better person to achieve the feat - I'll be delighted, records are there to be broken and it's not an issue for me.
"Shane has been a consistent and proven performer for Wales over the last ten years. I just hope he continues to score tries. When you play for Wales, you don't think about scoring tries and it's only something you look back on when you retire.
"In my day, Gerald Davies and myself did enjoy a bit of rivalry on who had scored the most but it's not the most important thing - winning Test matches is. But I really hope Shane scores against France and we win the match."
Williams, out of contract at the end of the 2011 season, admits he is flattered by the interest of big-spending Toulon. The cash-rich French club have made an audacious bid for the former IRB World Player of the Year.
Williams confirmed Toulon have held talks with his representatives and has refused to rule out linking up with England fly-half Jonny Wilkinson in the south of France. He added: "Of course, I am flattered by Toulon's interest in me. You have to be when somebody says they want you in their squad.
"Toulon are a big club with a big heritage and they are doing really well in the French League. But I'm still an Ospreys player at the moment."