The top-seeded Ferrer, bidding for his third singles title in Auckland, needed just 61 minutes to beat the big-serving Rosol and set up a quarterfinal against Colombia's Alejandro Falla.
Ferrer relied on his strong return game to beat the 6-foot-5 Rosol, converting three of four break points.
Olivier Rochus of Belgium struggled to beat sixth-seeded Thomaz Bellucci of Brazil 7-6 (6), 5-7, 7-6 (5) in a match that lasted more than three hours, while second-seeded Nicolas Almagro of Spain advanced comfortably, serving 11 aces to beat Santiago Giraldo of Colombia 6-4, 6-2.
Ferrer jumped ahead early in his match, breaking Rosol in the seventh game of the first set before serving the set out. The Spaniard then broke Rosol in the third and fifth games of the second set to take the match.
"I played good today, no? He plays with great power and it's good to start this way in the first match and to win in two sets," Ferrer said.
Kohlschreiber, the 2008 champion, had to battle for three sets for the second straight match, rallying from a set down to beat Harrison. The 19-year-old American had ousted Sam Querrey in the first round.
"It could be sometimes a little easier to go to three sets and at this stage of the season it's exactly what I need," Kohlschreiber said.