Hantuchova won five straight games to take the first set and lead 2-0 in the second.
The fifth-seeded Muguruza broke serve six times in her 6-3, 6-2 win over Stefanie Voegele of Switzerland.
Muguruza will face Peer, who overcame Patricia Mayr-Achleitner of Austria 7-6 (4), 4-6, 7-6 (3) in a match that lasted more than three hours.
Peer took a 4-0 lead in the final tiebreaker after Mayr failed to serve out the match at 5-4 and 6-5 in the last set.
The sixth-seeded Peng defeated Ukrainian qualifier Maryna Zanevska 6-4, 7-6 (5) to next play Hantuchova.
Zanevska made five double-faults and dropped serve at 5-4 in the first set. Peng rallied from a 5-2 deficit in the final set and led 5-1 in the tiebreaker.
In her return from injury, Polona Hercog of Slovenia cruised past seventh-seeded Zhang Shuai of China 6-2, 6-2 to move into the second round.
Hercog broke Zhang twice in the first set and three times in the second.
She has been sidelined by a right rib injury since the Australian Open where she retired in the first round because of a right shoulder injury.