Edinburgh centre-wing Tom Philip, Borders scrum-half Chris Cusiter and Edinburgh back-row forward Allister Hogg will represent the country for the first time.
"The three of them deserve this chance," said Williams. "They have done very well since the World Cup.
"A lot of players have retired since then and I have had to build a new side and I have confidence in these guys."
Captain Chris Paterson and vice-captain Gordon Bulloch will help the players through the test at the Millennium Stadium.
Williams has defended his decision to draft in three uncapped players and he is confident they can rise to the challenge.
He added: "I do have faith and to give them the opportunity of some experience is the only way for these guys to get better.
"We haven't the resources of the English and the French in terms of personnel and our plans are longer term.
"But sometimes we can be too cautious. It will be a great experience for them.
"I don't think I am throwing these guys in at the deep end. They know what it's like to play against Wales."
Philip's rise to prominence has been completed having forced his way into the European Cup hopefuls Edinburgh's team this season.
Williams said: "He is very powerful for his age and he has a big future ahead of him. There are other younger players but they are not as physically developed as Tom.
"He has those physical requirements. He doesn't have the experience and so we are giving it him."
Scotland team to play Wales in the RBS Six Nations Championship on Saturday, February 14 at the Millennium Stadium, Cardiff:
Ben Hinshelwood (Worcester); Simon Danielli (Bath), Tom Philip (Edinburgh), Brendan Laney (Edinburgh), Andrew Henderson (Glasgow); Chris Paterson (Edinburgh, captain), Chris Cusiter (Borders); Tom Smith (Northampton), Gordon Bulloch (Glasgow, vice-captain), Bruce Douglas (Borders), Scott Murray (Edinburgh), Stuart Grimes (Newcastle), Cameron Mather (Glasgow), Simon Taylor (Edinburgh), Allister Hogg (Edinburgh).
Replacements: Rob Russell (Saracens), Gavin Kerr (Leeds), Jason White (Sale), Simon Cross (Edinburgh), Mike Blair (Edinburgh), Dan Parks (Glasgow), Simon Webster (Edinburgh).