World number seven and French Open finalist Paolini, 28, who had never won a match on grass before this year, beat American world number 19 Emma Navarro in straight sets, 6-2 6-1.
She will face Croatian word number 37 Donna Vladic in the semi-final on Thursday.
“It’s incredible, it’s crazy to have won on this court,” said the Tuscan after her first match on Centre Court.
“I’m so happy I don’t know what to say at the moment.
“It’s special to be in the semi-final here, becoming world number five is incredible.”
Paolini said it was her “dream” ever since watching Wimbledon as a little girl.
“It’s a dream to play these matches,” she said.
ANSA