In a fourth-round match that began about 11 p.m. Wednesday ET and lasted until about 2 a.m. Thursday, Nadal climbed back after losing the first set and falling behind 3-5 in the second. He then overcame four match points in the ninth game, and another in the 10th.
The 22-year-old Spaniard broke Nalbandian's service to pull even at 5-5, then both held. Nadal shot out to a 4-0 lead on his way to winning the tiebreaker and the set.
He then dominated the third set against the Argentine, who had beaten him in both their previous meetings.
"I was lucky," Nadal said. "I didn't go into the match with the best mentality. I didn't have a clear idea of how to play him, probably because I lost the last two matches against him. I have to play my game, and I didn't.
"I had a big save today. I hope to play more aggressive now."
Federer, his play spotty but good enough to continue his domination of his frequent foe, ousted Gonzalez 6-3, 5-7, 6-2.
Andy Roddick, the lone American remaining in the singles draw, came back strong in the third set to beat David Ferrer 7-6 (5), 3-6, 6-3. Roddick finished with 10 aces against his Spanish opponent, who served eight of his own.
Roddick, ranked No. 7, had difficulty handling Ferrer's service returns in the second set, but he won 15 of 18 first serves in the third.
"My rhythm on my serve went off in the second set and I guess I was developing a pattern," Roddick said. "But he played well. I thought I hit the ball well in the second set.
"The guy's a bulldog and he just does the basics so well. He's a good player."
Andy Murray also advanced, extending his fine 2009 start to 18-1 when Tommy Robredo retired in the second set of their match because of a wrist injury. Murray won the first set 6-2 and was up 3-0 in the second.
Defending champion and No. 3 Novak Djokovic outlasted Stanislas Wawrinka 7-6 (7), 7-6 (6). Juan Martin Del Potro defeated John Isner 7-6 (4), 7-6 (3), and Ivan Ljubicic downed Igor Andreev 4-6, 7-6 (5), 7-6 (4). Fernando Verdasco defeated Philipp Kohlschreiber 6-4, 3-6, 6-1.
Federer meets Verdasco and Murray faces Ljubicic on Thursday, with Nadal to play del Potro and Roddick to play Djokovic on Friday.
On the women's side, No. 11 Victoria Azarenka knocked off No. 2 Dinara Safina 6-7 (4), 6-1, 6-3 in a quarterfinal match. A 19-year-old from Belarus, Azarenka won titles at Brisbane and Memphis earlier this year. She is the No. 8 seed in the Indian Wells event. Safina, a 22-year-old Russian, was the top seed.
Federer, ranked No. 2 after losing his four-year hold on the top spot to Nadal last year, was inconsistent against No. 17 Gonzalez. The Chilean fought his way back into the match in the second set, overcoming earlier frustration he had vented by slamming a racket onto the court -- three times -- and shattering it.
Federer, the tournament champion three consecutive years beginning in 2004, said he felt he finally was able to establish some rhythm in his game after playing mostly serve-and-return against his first two opponents.
"Today was a bit more baseline, even though I couldn't find his [Gonzalez's] backhand," Federer said. "If you don't find his backhand, the point is over quickly. He has such a massive forehand.
"I'm looking forward to playing against Verdasco. It's a good thing that I'm still in the tournament and facing an opponent who actually is going to extend the rallies a little bit."
Murray, ranked No. 4, said he anticipated a difficult test heading into his match against Robredo.
"I was expecting a tough match. I had lost to Tommy two previous times I played him," the 21-year-old Scot said. "I knew I had to be on my game."
Murray said he was aware Robredo had a problem with his wrist, although he still seemed to be hitting the ball OK.
"But mentally, a wrist problem can be tough," Murray said. "I know because I've been through it. It's just the pain that's there and feeling like something might happen."