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Federer booked his place in the semi-finals with a ruthless 6-3 6-2 victory over big-serving Juan Martin Del Potroof Argentina before Nadal fought back to beat David Nalbandian, also of Argentina, 4-6 7-5 6-4.
Saturday's other semifinal will pit Serbian world No 1 Novak Djokovic against 11th-seeded American John Isner, both players having advanced on Thursday.
Second seed Nadal was delighted to scrape through, saving two break points in a gripping 10th game of the third set before sealing victory with a forehand drop shot to end an absorbing baseline rally.
Nalbandian, on the run, sent his attempted backhand return well wide and Nadal punched the air in delight as the stadium court erupted after a riveting encounter lasting two hours, 39 minutes.
"It was a very difficult match for me," the second-seeded Spaniard said in a courtside interview after almost blowing a 5-2 lead in the final set.
"I started a little bit more nervous than usual against a tough player like David. He's beaten me a few times in the past so it was a very important victory for me.
"I am very excited to be back here," added left-hander Nadal, who has reached the semifinals in his last seven attempts at Indian Wells.
Nadal will face Federer for a 28th time in Saturday's semi-finals, but it will be their first ever meeting at Indian Wells.
"I am playing probably against the best (player) in history," said the Spaniard, who holds an 18-9 career advantage over the Swiss.
"And because I played probably the most important matches in my career against him and probably him against me, that's why it makes the match a little bit more special than the rest."
Federer agreed: "I have had some great matches with him all around the world by now. He has such great movement that this is a court that works well for him. I would expect a difficult match."
Nalbandian, whose last victory over Nadal came at the 2007 Masters Series event in Paris, broke the Spaniard in the 10th game of the match when he hit a searing forehand winner down the line to take the opening set.
It was the first set Nadal had dropped in the tournament, having breezed through his first three matches for the loss of just 14 games at the hard-court venue.
The second set went with serve until Nalbandian was broken in the 11th game after netting an attempted backhand drop shot to trail 30-40 and then double-faulting. Nadal comfortably held serve to level the match.
The Spaniard seized control in the third set, breaking the Argentinian in the first and seventh games to lead 5-2.
Nadal was then broken while serving for the match in the eighth, squandered a match point in the ninth and finally sealed victory on his second opportunity after an absorbing 10th game.
Swiss world No 3 Federer broke ninth seed Del Potro once in the opening set and twice in the second to wrap up his win in just over an hour at the Indian Wells Tennis Garden.
Federer, who powered down 13 aces in a one-sided match, completed his fifth successive straight-sets victory over the tall Argentine when his opponent netted a forehand service return.
"This was for me a really good match against a great player," the 16-times grand slam champion said after beating Del Potro for the fourth time this season.
"I'm happy I was happy to maintain the great streak I've got going against him this year. He's a top-10 player, a very dangerous player."
Federer, who had battled flu and a temperature to beat his first three
opponents at Indian Wells, has won 37 of his 39 matches since last
year's US Open.
