Playing under the closed roof of Hisense Arena due to the extreme heat that had earlier suspended play on the uncovered courts, Federer raced through the first set in 26 minutes with a strong service game and by belting 17 winners.
Federer's sixth ranking - courtesy of a sub-par 2013 - had given the impression of a 32-year-old man whose skills may be diminishing as he enters the twilight of his illustrious career.
That presumption was emphatically rejected when Kavcic held two break points in the fourth game of the second set and had Federer scrambling back and forth in a 23-shot rally only for the Swiss to force a forehand error.
The hard-hitting world number 99 simply stood hands on hips slowly shaking his head as if pondering what to do next.
The Slovenian did manage to break on the next point and thrust his arms skyward in mock triumph, though that only served to fire up Federer who won 13 of the next 16 points to clinch the set in 28 minutes.
The third set was a little closer with Kavcic's serve improving markedly but he could not halt the inevitable as Federer ended the 107-minute lesson when he clinched the tie-break 7-4.
Federer will now meet either 31st seeded Spaniard Fernando Verdasco or Russian Teymuraz Gabashvili in the third round.
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