The 2010 Casablanca champion dropped the first set but then rebounded for a 4-6, 6-2, 6-1 victory over Kavcic on the clay courts of Complexe Al Amal.
Frenchman Benoit Paire also reached the quarters, rallying to get past Slovenian Aljaz Bedene 4-6, 6-4, 6-3.
He will next face Spain's Tommy Robredo, who cruised past German Tobias Kamke 6-4, 7-5.
Seventh-seeded Robin Haase of the Netherlands and Frenchman Kenny De Schepper each registered a first-round win Wednesday.
Ohio bar shooting arrested, charged with murder
McPhee, Cokas 'working on their marriage' after affair