Rosol had not tasted victory on the ATP Tour since clinching his second career singles title at the Winston-Salem Open in August.
However, the Czech proved far too strong for Slovakia's Lukas Lacko in their first-round meeting on Wednesday, prevailing 6-2 6-4 in a shade over an hour.
Rosol will nevertheless be eager to sharpen up in his second-round tie with Viktor Troicki after landing just 46 per cent of his first serves against Lacko, who was still unable to carve out a break point.
Home favourite Melzer, champion in Vienna in 2009 and 2010, saw his hopes of a third title go up in smoke with a defeat to sixth seed Ivo Karlovic.
Both players had battled through three-set first-round matches on Tuesday, but Melzer found himself overpowered on this occasion as Karlovic amassed 21 aces on his way to a 6-4 7-6 (7-1) triumph.
When the Croat did come under pressure, he held firm, saving each of the three break points he faced.
The other seed in action on Wednesday, Germany's Philipp Kohlschreiber, found himself a set down to Carlos Berlocq but recovered to win 3-6 6-1 6-4 and book a place in the third round.
Tobias Kamke demonstrated similar resilience, beating Simone Bolelli 3-6 6-3 6-4 to set up a second-round meeting with David Ferrer, while Sergiy Stakhovsky is also through to round two after a 6-2 4-6 6-3 victory over qualifier Miloslav Mecir.