The Scots were dealt a blow when Cameron Mather (ankle) and Tom Smith (hip), both injured against England in the 35-13 defeat at Murrayfield, failed to recover in time.
Williams drafted in Edinburgh duo Allan Jacobsen and Allister Hogg as replacements.
Scotland team to play Italy in Rome on Saturday, March 6
B Hinshelwood (Worcester); S Danielli (Bath), T Philip (Edinburgh), B Laney (Edinburgh), S Webster (Edinburgh); 10 C Paterson (Edinburgh, capt), C Cusiter (Borders); A Jacobsen (Edinburgh), G Bulloch (Glasgow), B Douglas (Borders), S Murray (Edinburgh), S Grimes (Newcastle), J White (Sale), S Taylor (Edinburgh), A Hogg (Edinburgh).
Replacements: G Kerr (Leeds), R Russell (Saracens), N Hines (Edinburgh), J Petrie (Glasgow), M Blair (Edinburgh), A Henderson (Glasgow), D Lee (Edinburgh).