The Slovakian took to the clay court late in the day but had no problems getting past Spaniard Lourdes Dominguez Lino 7-5 6-2 at the WTA International event.
Dominguez Lino, the beaten finalist in 2013, battled hard throughout but was unable to find the form of last year as Hantuchova had too much in the important moments.
The world number 30 will now face sixth seed Shuai Peng in the next round, after the Chinese recorded a comfortable victory over Maryna Zanevska.
Peng sealed her progress courtesy of a 6-4 7-6 (7-5) victory in 94 minutes, but the win could have come sooner had she not missed a match-point chance at 6-5 in the final set.
Meanwhile, Patricia Mayr-Achleitner of Austria was unable to recreate the form that saw her beat Elina Svitolina in the first round as Israel's Shahar Peer won a gruelling match 7-6 (7-4) 4-6 7-6 (7-3).
In over three hours on court both players broke and were subsequently broken several times as the momentum shifted at regular intervals.
Peer eventually had enough to seal victory though, converting her first match point in the final set tie-break.
Also in the second round, fifth seed Garbine Muguruza wasted little time in beating Swiss opponent Stefanie Voegele 6-3 6-2.
The Spaniard took just over an hour to claim the win, showing her resilience by saving five of seven break-point chances she offered up.
Voegele, by contrast, gave up her serve on six occasions - while she also had no response to the power of her opponent, who fired down five aces throughout the match.
There was also one final first-round match completed on Wednesday, as Polona Hercog caused an upset by beating seventh seed Shuai Zhang of China 6-2 6-2.