Spaniard Nadal, twice champion at Indian Wells, was gifted his spot when Argentina's Leonardo Mayer withdrew with a back injury before the start of their third-round match.
Federer, a four-times winner of the ATP Masters 1000 event, progressed with a commanding 6-3, 6-1 victory over Croatia's [ Images ] Ivan Dodig in a contest lasting just 61 minutes.
Nadal will meet Latvian Ernests Gulbis [ Images ], who fought back to beat Italy's [ Images ] Andreas Seppi 5-7, 6-3, 6-4, while Federer faces fellow Swiss Stanislas Wawrinka or Australian Lleyton Hewitt [ Images ].
Wawrinka and Hewitt were scheduled to play later on Monday.
Nadal, who is competing in his first tournament on a hardcourt surface in almost a year, was saddened when he learned that Mayer had withdrawn.
"That's bad news, for sure, for the fans and for Mayer, especially," the world number five told reporters at the Indian WellsTennis Garden. "I talked with him. It seemed like it's nothing very, very bad.
"Just a typical back problem, beginning when he was warming up his serve. The physio says maybe in four days, five days he will be ready.
"That's the most important thing, that nothing is serious," said the Spaniard, who was sidelined for seven months last year by a left knee injury.
Though Nadal has beaten Gulbis in their four previous meetings, the Latvian looked forward to challenging the Spaniard after winning his 13th consecutive match on Monday.
"When was the last time I won 13 matches in a row?" 67th-ranked Gulbis said. "Of course he's a great player, but I honestly believe that if I play my best game I can beat him.
"I like to play against him because his ball and his heavy spin, it's good for my timing. I don't like it when the opponents hit flat, deep balls."
Second-seeded Federer, the defending champion at Indian Wells, improved his win-loss record this year to 12-3 after overcoming Dodig in their first meeting.
Dodig gave the Swiss a tough challenge early on and the opening set went with serve until the eighth game when the Croatian made two consecutive double faults to be broken.
Federer then needed four set points to serve out, finally clinching the set in 34 minutes with a service winner that left his opponent floundering.
The Swiss maestro then took firm control, breaking Dodig in the first game, when the Croatian netted a backhand, and also in the third, when his opponent again double faulted.
Federer sealed victory by breaking Dodig for a third time, the match ending on yet another double by the 60th-ranked Croatian.
In other matches, sixth-seeded Czech Tomas Berdych eased past Germany's [ Images ] Florian Mayer 6-4, 6-1 while 10th-seeded Frenchman Richard Gasquet swept aside Poland's Jerzy Janowicz 6-1, 6-4.
Photograph: Danny Moloshok/Reuters