The fourth-seeded Austrian, who had a bye in the first round, broke De Voest's serve four times at Putra Stadium.
"The first set was one of the best sets I've played all year," Melzer said.
Dmitry Tursunov of Russia reached his third quarterfinal of the season by defeating Belgian wild card David Goffin 6-3, 6-3. Marcos Baghdatis also advanced, stopping Somdev Devvarman of India 7-5, 6-4.
The 96th-ranked Cipolla saved five of six break points to beat the Wimbledon quarterfinalist. The 18-year-old Tomic became the youngest player since 1986 to reach the Wimbledon quarterfinals this year.