Wales had dreams of back-to-back Grand Slams wrecked by a heavy defeat to England last weekend.
But Scotland's stunning victory over pre-tournament favourites France blew the championship wide open, and Williams has demanded Wales take maximum advantage against the Scots in the Millennium Stadium.
"It's a massive game on Sunday. We have three homes games to come and we haven't given up on the championship yet, but after last week we need to get a win on the board," said British & Irish Lion Williams.
"If we can do that with the style of last year then that would be great, but I'd be happy to win ugly."
Scotland's victory over France surprised many, but not Williams. Four hours before kick-off he predicted: "I think they will be the dark horses in this championship."
And so it proved. France were not prepared for Scotland, a side with just one victory in the last two Six Nations, to put them under such intense pressure.
Scotland played high-tempo rugby, their rolling maul was dominant and Frank Hadden's men overpowered the French en route to a famous 20-16 victory.
Williams assured Wales fans there is no danger of his side underestimating Scotland in the same way.
"I did say they would be the dark horses and that win didn't surprise me at all," he added. "They have been steadily improving and it will be a big challenge for us this weekend.
"They have probably been saying all week that the win over France means nothing unless they can back it up with a victory over Wales."
Wales stayed with England for 50 minutes at Twickenham last weekend before the world champions emptied their experienced bench and ran away with the game, scoring 29 unanswered points in the last quarter.
Wales head coach Mike Ruddock has kept faith with the same starting XV but improvements have been demanded across the board and fly-half Stephen Jones is confident they will bounce back in style.
"It was a huge disappointment last week, but there is a lot more to come from us. We have worked particularly hard this week on improving our weaknesses and hopefully we can put that right on Sunday," he said.
"Our attacking game wasn't up to scratch last week but we need to control the contact area and our continuity would be better.
"These are all things within our control and we can fix the negatives. We must improve and we need to repay the coaches' confidence with a win.
"There is a great team spirit. We have a self belief and a confidence that from working hard in the week we can put a good performance together."