The world number one raced into a 5-3 lead but had to save two break points to hold serve before clinching the first set.
Williams, who has yet to drop a set in the tournament, broke early in the second but her opponent was in battling mood and responded to level at 3-3.
Hantuchova's hopes were short-lived, however, as Williams seized the initiative in the Slovakian's next service game and served out for the victory, sealing it with a powerful forehand winner on her fourth match point.
"It was a tough match," said Williams. "Daniela is a great opponent so I'm really happy to come out with the win. It was hot but you have to play, you have to be ready and prepare yourself mentally. I'm excited to get through."
Serena and sister Venus Williams later withdrew from the doubles shortly before their first-round match because of an injury to Venus's left leg.
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