Vinci, who titled at s'Hertogenbosch in 2011, breezed into the second round with 6-3, 6-3 decision over Estonian Kaia Kanepi. She next faces last week's Nuremberg, Germany, titlist Simona Halep.
Spain's Suarez Navarro, meanwhile, posted a second-round triumph over Sweden's Sofia Arvidsson 6-3, 6-4 at Autotron Rosmalen.
Her next opponent will be Bulgarian Tsvetana Pironkova, who bested Romanian Irina-Camelia Begu 7-6 (9-7), 6-2 Tuesday.
Joining them in the quarterfinals was seventh-seeded Pole Urszula Radwanska, who moved on when opponent Magdalena Rybarikova of Slovakia retired in the first set.
Fourth-seeded Belgian Kirsten Flipkens and Ukrainian Lesia Tsurenko each posted a first-round victory Tuesday.