Fourth seed Novak Djokovic also reached the last eight with a 7-5, 6-3 win over Jeremy Chardy of France.
One more win apiece for Federer and Murray and they will be squaring up to each other in the semi-finals.
On Thursday, they enjoyed very different paths through to the last eight.
Swiss world number one Federer had to come from 3-1 down in the final set to beat Spaniard David Ferrer 3-6, 6-3, 6-4, while number two Murray hammered Czech Radek Stepanek 6-4, 6-1.
Ferrer had won just one set in eight previous meetings with Federer but it was the top seed whose game was all over the place early on.
A blustery wind caused both players trouble but after trading early breaks world number 19 Ferrer broke again in the eighth game and served out for the opening set.
Federer pulled himself together in the second set to level the match but a real surprise looked possible when he was broken and trailed 3-1 in the decider.
He broke back immediately and from that point on there was only going to be one winner, with a beautiful backhand topspin lob sealing the vital break in the eighth game.
GREAT MATCH
"I didn't think I was going to (turn it around) because I thought David was playing a great match," Federer said.
"I think at the beginning maybe my footwork was just a touch off. After that I think I got it together and started to play better and better."
In the quarter-finals, Federer will play former world number one Lleyton Hewitt after the Australian saw off American Sam Querrey 6-1, 2-6, 6-3.
Title-holder Murray was on top of his game as he destroyed the hopes of world number 17 Stepanek in just 76 minutes.
The Czech recovered from 5-2 down to get back on serve at 5-4 but Murray broke again to win the set thanks to a stunning top-spin lob on the run, before blitzing through the second.
"I started the match very well, serving well and not giving him any chances," Murray said. "Then the wind picked up at the end of the first set and he managed to break me.
"But I played a good game to break back. Had a couple of good returns and obviously a lob to finish with was nice. After that, I started to feel a lot better but it was tough conditions, very, very windy."
Murray will play Julien Benneteau in the last eight after the Frenchman became only the third lucky loser to reach the quarter-finals of a tournament since tennis turned professional in 1968, beating Spaniard Guillermo Garcia-Lopez 4-6, 6-4, 7-6.
In just his second event after two months out with knee injuries, Nadal recovered from a slow start to beat Frenchman Paul-Henri Mathieu 7-5, 6-2 in the night match.
Mathieu produced an early onslaught as he surged ahead 4-1 but Nadal bounced back superbly to win five of the next six games and take the set.
After a tight start to the second, Nadal broke in the fourth game and again in the sixth on his way to victory and a quarter-final against Czech Tomas Berdych, a 6-4, 6-3 winner over Australian qualifier Chris Guccione.
Djokovic will play ninth seed Gilles Simon after the Frenchman edged out eighth seed Nikolay Davydenko of Russia 6-7, 6-4, 6-4.