Paolini's victory ensured she eclipsed compatriots Camila Giorgi (2018), Francesca Schiavone (2009), Silvia Farina Elia (2003) and Laura Golarsa (1989), who had all reached the quarter-finals at the grasscourt Grand Slam in the Open era.
Navarro drew first blood in the third game with a forehand rocket but Paolini responded immediately and the French Open runner-up then ramped up the pressure after some heavy exchanges from the baseline to pull away for a 5-2 lead in the opening set.
The diminutive Italian mixed things up against her American opponent to comfortably win her fifth straight game and take the first set in double quick time on Centre Court.
Navarro, who had never lost in three previous meetings with Paolini, gave herself a fighting chance with two break points in the third game of the next set but the 19th seed was unable to convert either.
Her hopes of reaching a first Grand Slam semi-final faded further as Paolini took a 5-1 lead, having staved off another comeback attempt.
Paolini wobbled slightly as she looked to land the knockout blow on serve but a wayward shot from Navarro sent her through.
