The top-seeded Spaniard broke in the first game of each set against the big-serving Ebden, who was playing only his 11th match at this level.
The 23-year-old Australian didn't appear overawed by the occasion and had a point to break back at 3-2 in the second set, but Nadal weathered the threat to move into the third round where he will meet Radek Stepanek.
Second-seeded Andy Murray was another second-round winner, beating Xavier Malisse 6-3, 5-7, 6-3.
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