Kartal has made a brilliant return from six months out with a back injury and dropped only two games in a 6-2 6-0 victory on Thursday against the 15th seed Paolini to storm into the quarter-finals.
It was an error-strewn performance from former French Open and Wimbledon runner-up Paolini and Kartal took full advantage, winning the final 11 games.
On Wednesday, top-seeded Aryna Sabalenka and second-seeded Jessica Pegula had both lost their second-round matches.
Kartal's win equalled the 24-year-old's best performance at a WTA 1000 tournament – the top level of the women's tour – with the Briton also having reached the last-eight in Beijing last year.
She will next face fifth seed Elina Svitolina, who broke Guo Hanyu's serve in the opening and final games of the match to beat the Chinese wildcard 6-1 6-4.
Surprise French Open runner-up Maja Chwalinska is also through to the quarter-finals after a 6-4 6-1 win over 10th seed Iva Jovic, while Diana Shnaider defeated sixth seed and Wimbledon finalist Karolina Muchova 7-5 6-3.
Iga Swiatek kept up her push to qualify for the WTA Finals as she ground out a 6-1 6-4 win over American lucky loser Ashlyn Krueger, who managed to put some pressure on the Polish great despite racking up 44 unforced errors.
Swiatek will next face another American in the quarter-finals after Ann Li, the conqueror of Sabalenka, eliminated Indonesia's Janice Tjen 6-1 7-6 (7-1).
12°C