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.
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.