The Italian never managed to seriously threaten Wawrinka's serve until the 12th game of the second set, when he broke the Swiss to force a tiebreak.
He then fought off three match points before finally succumbing 10-8 to the No. 10-ranked Wawrinka, who next plays Jeremy Chardy.
Second-seeded Dominika Cibulkova reached the women's quarterfinals by coming from a set down to beat Anabel Medina Garrigues 2-6, 6-4, 6-3.
Earlier, the last two remaining Dutch players lost their second-round matches. Kirsten Flipkens beat Michaella Krajiceck in two hard-fought sets 7-6 (6), 7-6 (3), and Evgeny Donskoy overcame Robin Haase 6-4, 7-5.
Results from day four of the 's-Hertogenbosch ATP/WTA (x denotes seeding):
Guillermo Garca-Lopez (ESP) bt Daniel Brands (GER) 7-6 (9/7), 6-2
Stanislas Wawrinka (SUI x2) bt Paolo Lorenzi (ITA) 6-3, 7-6 (10/8)
Jeremy Chardy (FRA x5) bt Marius Copil (ROM) 7-5, 6-4
Roberto Bautista (ESP) bt Carlos Berlocq (ARG) 6-2, 6-3
Evgeny Donskoy (RUS) bt Robin Haase (NED) 6-4, 7-5
Nicolas Mahut (FRA) bt Andrey Kuznetsov (RUS) 6-2, 6-4
Jan Hernych (CZE) bt Michael Llodra (FRA) 6-7 (5/7), 6-4, 7-5
Lesya Tsurenko (UKR) bt Stefanie Vogele (SUI) 6-1, 7-6 (7/4)
Kirsten Flipkens (BEL x4) bt Michalla Krajicek (NED) 7-6 (8/6), 7-6 (7/3)
Garbine Muguruza (ESP) bt Lauren Davis (USA) 6-2, 6-0
Dominika Cibulkova (SVK x2) bt Anabel Medina Garrigues (ESP) 2-6, 6-4, 6-3