Head coach Frank Hadden has been warning his troops all week that such a famous victory will count for nothing if they cannot back it up with a first away win in eight championship attempts.
But while Scotland are trying to build a reputation, Sunday's game is crucial for a Wales side determined to preserve their status as one of the leading forces in world rugby.
Injuries and suspensions have undermined their Six Nations defence and a heavy defeat to England last week shredded any dreams of back-to-back Grand Slams.
Williams described the contest as "massive as far as Wales are concerned" - massive in the context of the 2006 RBS 6 Nations, and massive in terms of proving Wales are not one-season wonders.
"We want to give a performance to show we are just as good as last year, if not better, and that the England result was a one off," he said.
"It will show how mentally strong we are having lost last weekend - and I am confident we can beat them.
"Scotland deserve to be on a high. Beating France was a massive win for them, and we experienced that last season, but it is only one win.
"Scotland played well on the day but France can play a lot better - there are two ways you can look at it."