Despite her victory, Vinci was keen to heap praise on her 21-year-old opponent.
"Camila played flat but I served really well and won lots of points that way," Vinci told reporters.
"Camila is a great player and had nothing to lose after winning three matches in qualifying and three in the main draw. She is one for the future.
"I had lots of points to defend, so I am happy to get to the quarter-finals again."
Vinci will face another fellow Italian Flavia Pennetta in the last eight.