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.
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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.
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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
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