Kavcic defeated Thanasi Kokkinakis 6-4, 6-2 without dropping his serve. He dropped 16 points over his nine games serving and saved all three break points Kokkinakis managed.
Kokkinakis, 17 years old and ranked No. 397, was given a wild-card spot into the tournament.
The win advanced Kavcic into the second round against top-seeded Richard Gasquet. The top four seeds, who include No. 2 Jo-Wilfried Tsonga -- the tournament defending champion -- were given first-round byes.