Rain affected play in Lugano, Switzerland, for the fifth successive day, but Mertens eventually won through 6-2, 5-7, 7-5 to advance to the last eight.
"With the rain, it's not easy just to come on, come off court, but it was a really close match and I'm happy I won it in the third," Mertens told the WTA's official website after her match. "I tried to keep up my game, but of course it was difficult. We were both competing well in the third set."
Sixth seed Alize Cornet and eighth seed Aliaksandra Sasnovich were not so lucky, losing to Stefanie Voegele and Kirsten Flipkens respectively. Home favourite Voegele came from a set down to win 2-6, 7-5, 6-3, and Flipkens secured a 4-6, 6-4, 6-2 triumph.