Following both their victories, the two champions now increased their odds to face each other in the semifinals to fill fans with excitement.
Nadal, meanwhile, himself a 17-time Grand Slam champion and the current world number four, beat Serbia's Filip Krajinovic 6-3, 6-4 in one hour and 26 minutes.
Andreescu will get a shot at another top-10 player in the semi-finals, after sixth-ranked Elina Svitolina clawed out a 4-6, 6-4, 6-4 victory over another red-hot teen - Marketa Vondrousova of Czech Republic.
Elsewhere, Hubert Hurkacz upset Nishikori 4-6 6-4 6-3 to set up a meeting with Denis Shapovalov.
Born in Canada, Andreescu first took up tennis at age 7 in Romania, where her parents worked. Maybe because of the conditions, [it was] windier out there today. On the tiebreak, I started to go again a little bit higher intensity and tried to push myself to serve faster. "That's where I got my good feeling and my good tennis and also the good physical health back".
Kecmanovic became the first lucky loser to reach the last eight at Indian Wells since the ATP's Masters 1000 series launched in 1990.
"It will be amusing that somebody other than Novak is still in", Kecmanovic said of top-ranked Djokovic, his famous countryman who was upset on Tuesday.
A five-time champion at Indian Wells, Federer's first meeting with Kyle Edmund was straightforward, claiming a 6-1 6-4 win.
Kecmanovic, who gained entry to the second round when fifth-seeded Kevin Anderson withdrew with an elbow injury, is in his first ATP quarter-final.
Federer will face Hurkacz for the first time in the quarterfinals. "I hope I can get there, but I am not going to underestimate Hurkacz".
In the evening, Gael Monfils stretched his best start to a season to 15-3 after dominating Philipp Kohlschreiber 6-0, 6-2.
Kecmanovic presses on A day after world No. 1 Novak Djokovic tumbled out of the third round, 19-year-old Miomir Kecmanovic kept the Serbian flag flying.