The top-ranked Nadal hammered his fellow Spaniard with hard groundstrokes, cruising to victory after breaking Gimeno-Traver's first two service games.
"The first days of a tournament are always dangerous. But I feel fine," Nadal said. "It was not one of those matches that pushed you to your limits."
Nadal, who sat out last year's event after winning five straight titles from 2005-09, will face Santiago Giraldo of Colombia in the third round of the outdoor clay-court event.
"[Giraldo] is very aggressive and one of the most dangerous players on the circuit," said Nadal, who has beaten his upcoming opponent in straight sets in their previous two meetings.
"The match against [Giraldo] last year was hard. Tomorrow I have to play solid and be as aggressive as I can," he said.
Soderling, last year's finalist, went out in the third round of the Masters events in Indian Wells and Miami last month.
Dodig, who won his first title at Zagreb earlier this year, goes on to face 15th seed Milos Raonic. The Canadian beat Germany's Simon Greul 6-3, 4-6, 7-6 (5).
Two-time finalist Ferrer saved all four break points he faced, despite not serving well.
"I think I began a little more nervous than usual, but that is logical since it is the first match," Ferrer said. "Fortunately I was able to handle it and I hope to do better tomorrow."
At 2-1 in the first set, Melzer asked for a doctor to check his pulse, but he continued to play and won the next three games.
The former top-ranked player hit three aces in his second match since returning to the court after undergoing wrist and knee surgery in October.
"I was a little worse physically due to being tired from yesterday, but I held up well," said Ferrero, who will play Simone Vagnozzi in the next round after the Italian bounced Juan Monaco of Argentina 6-3, 6-2.