Lukas Lacko dumped Sofia Open eighth seed Evgeny Donskoy out in the first round on Monday.
World number 96 Lacko produced an assured display at the ATP 250 event, with a break in each set proving the difference.
Home hope Dimitar Kuzmanov, ranked 340th, put up a resilient first-set showing against seventh seed Joao Sousa before going down 7-6 (8-6) 6-1 in the only other main-draw match.
Sousa is in the same half of the draw as headline act Stan Wawrinka, who is yet to learn the identity of his second-round opponent.
In Montpellier at the Open Sud de France, Benoit Paire beat Mischa Zverev 6-4 6-4, while sixth seed Andrey Rublev prevailed by the same scoreline against Guillermo Garcia-Lopez.