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The former world number one got the better of his Slovenian opponent 6-2 6-1 7-6(4) in the second round on Thursday.
Federer took just 26 minutes to win the first set 6-2 at the Hisense Arena and only 28 to romp to a 6-1 victory in the second.
However, the third was more competitive as 26-year-old Kavcic stepped up his game, with Federer committing 17 unforced errors.
The third set went to a tie-breaker, which also proved to be tight, but in the end Federer came out on top 7-4 to progress to the third round of the tournament.