Nadal topped Florent Serra of France 6-2, 6-4, and eighth-seeded Nalbandian downed Nicolas Kiefer of Germany 7-6 (5), 6-3.
Federer had the most trouble, saving two set points in the tiebreaker to beat Robin Soderling 6-4, 7-6 (7).
"He's got a big serve, really suits the indoors well,'' Federer said. "I'm happy to be through, kind of a relief for me. I was surprised he didn't return a bit better, but I think I've been really serving well lately, basically since the U.S. Open.''
Soderling won the Lyon Grand Prix on Sunday but lost for the eighth straight time to the Swiss star.
The Swede had set point at 6-5 on serve but hit a forehand wide. He got another chance after the next point but didn't take it again and his long forehand gave Federer match point.
Federer is enjoying the end to a tough season, getting a win at the Swiss Indoors in Basel last week to add to an Olympic gold medal in doubles and the U.S. Open title for his 13th major.
"I'm happy the way things have gone this season after kind of a rough start and a rough Wimbledon final,'' said Federer who lost that final to Nadal. "So I've really been able to turn around, you know, get some emotional wins with the Olympic gold and Basel again and then the U.S. Open.''
Also second-round winners were fourth-seeded Andy Murray, sixth-seeded Nikolay Davydenko, 10th-seeded Gilles Simon, 11th-seeded James Blake and 13th-seeded Jo-Wilfried Tsonga. No. 5 David Ferrer and No. 12 Stanislas Wawrinka were upset.
Nadal was looking forward to facing No. 16 Gael Monfils of France for the first time in nearly 2 1/2 years.
"(Monfils) is playing very well this year,'' Nadal said. "He can play aggressive, sometimes he plays defensive, two meters behind the baseline. He can do something different.''
Federer will play Marin Cilic of Croatia, and Nalbandian will meet Juan Martin del Potro for the third time in three weeks.
"That is a little bit strange,'' Nalbandian said of facing his fellow Argentine. "It's going to be a tough one, we both know each other very well.''
Nalbandian beat del Potro in the semifinals of the Swiss Indoors last week, after del Potro won in the Madrid Masters third round.
Murray defeated Sam Querrey of the United States 6-2, 6-4 to stay on track for a record third straight Masters title after winning Cincinnati and Madrid.
Davydenko, the 2006 champion, advanced with a 7-6 (5), 7-5 win over Ivan Ljubicic of Croatia. He will play 2005 champ Tomas Berdych of the Czech Republic, who beat Wawrinka 6-3, 7-5.
Tsonga rallied to beat 2004 runner-up Radek Stepanek 3-6, 6-4, 6-4 and next faces No. 3 Novak Djokovic of Serbia.
"(Stepanek's) difficult to play because he has a very special rhythm,'' Tsonga said. "Sometimes he plays fast, sometimes slow, sometimes he changes the pace, and sometimes he plays shots no one would play.''
Djokovic beat Tsonga in the Australian Open final, then Tsonga paid him back somewhat by winning the Bangkok final.
Also, 10th-seeded Simon defeated Igor Andreev of Russia 6-3, 7-5 to keep alive his chances of reaching the eight-man Masters Cup in Shanghai. The Frenchman next faces seventh-seeded Andy Roddick of the United States, who was also vying for a Masters Cup spot.
Their hopes were improved when Ferrer lost 6-3, 6-2 to Philipp Kohlschreiber of Germany.
Kohlschreiber will play Blake, who kept alive his Masters Cup chance with a 6-7 (10), 6-3, 6-4 win over Simone Bolelli of Italy.
Cilic won 6-4, 7-6 (2) over Marcel Granollers of Spain.
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