Italy arrived at Murray field in buoyant mood, having beaten France last weekend.
However, the Italians were swept aside as Scotland secured their record Six Nations win and their first victory in the tournament for two years.
Meanwhile, Twelvetrees retained his place in England's starting line up as they travelled to Dublin to take on Ireland.
Weather conditions played a huge part in determining how the game panned out, with precious few try scoring opportunities created.
It came down to a battle of the boot, and Owen Farrell outgunned Ronan O'Gara as England triumphed by 12 points to 6 to leave Stuart Lancaster's side as they only side unbeaten after round two.