While four qualifying matches were played on the opening day of action, Kavcic's first-round encounter with Australian Thanasi Kokkinakis took centre-stage.
And world number 116 Kavcic was rarely troubled in a 6-4 6-2 victory that took just 77 minutes to complete.
The 17-year-old Kokkinakis – who is ranked 397th in the world and made his Davis Cup debut against France earlier this month – was granted a wildcard to the hard-court tournament.
But Kavcic's experience shone through as he won 14 of 18 points on first serve during the first set.
One break was enough for the winner to take the opener and he continued his momentum in the second set.
Kokkinakis was still proving a handful on first serve, but on his second attempts he won just one of eight points in the final set.
Kavcic converted both break points he earned himself en route to a comfortable victory.