The top-ranked Nadal needed only 46 minutes for the win, breaking Santoro three times in each set.
Federer advanced with similar ease, beating Potito Starace of Italy 6-2, 6-2, while defending champion Andy Murray defeated Albert Montanes 6-2, 6-4.
Federer converted four of his five breakpoints and was never in danger of losing his serve.
Murray dominated Montanes from the baseline and broke his serve in the third and fifth games to take the opening set in 40 minutes.
Montanes struggled with his accuracy throughout the match, committing 34 unforced errors as Murray used two more breaks in the second and will play Philip Petzschner of Germany in the next round.
Murray is coming off wins against both Nadal and Federer at an exhibition event in Abu Dhabi last week, and showed few signs of having lost his good form.
"Last week helped me settle down well in the match,'' said Murray, adding that he was still adjusting to playing at night in the Middle East. "It is tough when the sun goes down. It becomes windy. When the sun is out, the balls are pretty fast but when it goes down, your body becomes a little stiff and balls become heavy too. But I was OK for the majority of the match and I am happy about that.''
Federer played Potito Starace of Italy later Tuesday.
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