Federer needed just over an hour to dispatch Briton Kyle Edmund 6-1 6-4 in their first career meeting and reach the quarter-finals on a sunny and breezy day in Indian Wells.
Next up for the 20-times Grand Slam champion is another unknown quantity in Pole Hubert Hurkacz, who defeated Canadian teenager Denis Shapovalov 7-6(3) 2-6 6-3 earlier in the day to set up his first career meeting with the Swiss Master.
Nadal, 17 times a Grand Slam winner, ruthlessly put an end to Serbian qualifier Filip Krajinovic's run at the tournament, converting three of his four break point opportunities to advance 6-3 6-4.
Federer to auction off Grand Slam memorabilia
Neither Federer or Nadal have dropped a set in their three matches at Indian Wells, a tournament Federer has won five times and Nadal three.
Federer, who was playing the British number one for the first time, won 6-1 6-4 in one hour and four minutes.
Edmund’s nervousness was evident when he started his first service game with two double faults, quickly falling 5-0 behind the in the first set before eventually winning a game.
The second set was a closer affair, but Federer broke in the fifth game and got over the line.
Highlights: Djokovic dominates Nadal to take title
In other fourth-round action, hard-hitting Canadian Milos Raonic saved all three of Jan-Lennard Struff's break point opportunities to down the German 6-4 6-3.
The 13th seed will square off against France's Gael Monfils, a 6-0 6-2 winner over Germany's Philipp Kohlschreiber, in the quarter-finals on Thursday.
With additional reporting from PA Sport
Federer 'lagging behind' with fitness, but 'big titles' still the aim
Federer 'probably third or fourth best player on clay' but can he win Roland-Garros?