World number 52 Giorgi, 26, was on top of her game as she powered past Ekaterina Makarova of Russia 6-3, 6-4 as she set up a showdown against Williams on Centre Court.
Giorgi had only reached the last 16 at Wimbledon once before, in 2012, but she looked the part as she took the game to Makarova, ranked 36 and no. 1 in Ladies Doubles, producing five aces, some booming groundstrokes and fierce volleys in an excellent all-round performance on Court 12.
"I played a great match," she told a packed press conference, "very consistent and I played my game to a very good level."
Asked about her recent lack of progress up the rankings, she responded: "I've had many injuries over the past three years and many physical problems.
