The top seed had few problems in seeing off his Czech opponent this time, winning 6-2 7-6 (9/7) in one hour 44 minutes.
The Spaniard raced through the first set, breaking twice, before Rosol, who knocked Nadal out in a five-set thriller in the second round at Wimbledon, upped his game in the second.
Both players broke once, but it was Nadal who held his nerve in the tie-break to progress and set up a second-round meeting with Germany's Tobias Kamke.
Nadal's compatriot David Ferrer found the going rather tougher against Ukraine's Alexandr Dolgopolov and was made to work for a 6-3 5-7 6-3 win.
Ferrer, the second seed, broke once in the first set and twice in the third without dropping his serve.
The second, though, featured seven breaks of serve, with Ferrer broken four times to let his opponent back into the match.
Ferrer will play German Daniel Brands in the second round.
Defending champion Richard Gasquet had few problems as he beat Egyptian wildcard 7-5 6-1 to set up a second-round clash with fellow Frenchman Gael Monfils.
Andy Murray barely had to break sweat as he raced to a 6-0 6-0 win in a mis-matched clash.
The Wimbledon champion needed just 38 minutes to dispatch his 19-year-old opponent Mousa Shanan Zayed, the wild card ranked 2129 in the world.
The home favourite was way out of his depth against the third seed, who never had to get out of first gear as he continued his comeback from the back operation which curtailed his 2013 season.
Zayed won 17 points in the match and none on the Scot's first serve.
Murray, who was victorious in the men's doubles on Monday, was playing in his first Tour singles match since his injury lay-off as he looks to return to top form ahead of the Australian Open.
"It's good to be back," said Murray, for whom Florian Meyer of Germany is next up.
"I will probably go and hit a few balls with my coach (Ivan Lendl) now as it was quite windy and there were not a lot of rallies in the match."
Murray's compatriot Dan Evans went out in the opening round as he lost in three sets to Latvia's Ernests Gulbis.
Evans, the world number 150, had come through three rounds of qualifying to make the main draw, but was unable to spring an upset against the seventh seed.
Gulbis won 6-2 4-6 6-0 in one-and-a-half hours, breaking his 23-year-old opponent seven times in the match.
Germany's Philipp Kohlschreiber, the sixth seed, progressed with a 7-6 (9/7) 6-2 win over Spain's Pablo Andujar.
Also through to the second round are German duo Dustin Brown and Peter Gojowczyk.