The 22-year-old Pole is an accomplished doubles player and partnered Kristina Mladenovic to glory in Palermo this July but places a lowly 144th in the WTA singles rankings.
She lost the first set against the Belgian ranked 81 places above her but rallied to win 3-6 6-1 6-4 in under two hours.
Piter will tackle Annika Beck in the quarter-finals after the German defeated fifth seed Lucie Safarova 6-2 4-6 6-4 in the duchy.
Eighth seed Bojana Jovanovski reached the last eight with a comfortable 6-1 6-4 victory over Hsieh Su-wei. Top seed Caroline Wozniacki is a possible opponent, should the Dane conquer Monica Niculescu.
Czech qualifier Tereza Smitkova came through an outstanding first-round match against Mladenovic 7-5 6-1 but seventh seed Eugenie Bouchard was not so lucky, losing 2-6 7-5 6-1 to Germany's Andrea Petkovic.
In the doubles, Heather Watson partnered with Gabriela Dabrowski to upset British duo Nicola Slater and Melanie South 6-4 7-5. Nadia Petrova and Katarina Srebotnik await in the quarter-finals.