The Bulgarian, who had a bye into the second round, was put under pressure in both sets but needed just one match point to seal his tie-breaker victory.
Spain's Fernando Verdasco beat Jarko Nieminen of Finland 6-3, 6-4 to set up a quarterfinal match against Bernard Tomic.
The Australian beat third-seeded Kevin Anderson of South Africa 7-6 (4), 6-4. In first-round matches, Jack Sock of the United States defeated Andrey Golubev of Kazakhstan in three sets and France's Pierre-Hugues Herbert beat Pablo Carreno Busta of Spain.