She said "I played well today, especially in Group B. The Tunisians are here to support me so I feel like I'm at home."
Gaber, ranked 101st in the world, had difficulty in the first set, before her 21-year-old world champion easily surpassed the second.
Jaber has yet to lose any group in the finals, but she lost two sets in the qualifiers, which surpassed Hungary's Fanny Stollar, British Harriet Dart and Greece's Valentini Gramaticopoulou.
In the semi-finals, Gaber will meet Russian veteran Vera Zvonareva and Fifth-seeded Anastasia Sevastova.
In the rest of the quarterfinals, Belarusian Aleksandra Sassenovic is playing with Johanna Conta and Russian Anastasia Pavlyuchenkova with fellow sixth seed Darya Kasatkina.