Top seed Rafa Nadal destroyed local favourite Richard Gasquet 6-4 6-1 as he stepped up his bid for a record sixth Masters Series crown in the same season.
The Spaniard, who is chasing his 11th title of the year and is the only player left in the tournament not to have already won the indoor event, next faces compatriot and title holder David Ferrer or 2005 champion Tomas Berdych.
Federer, who had lost his last three encounters with the towering Del Potro including the Basel Open final on Sunday, defeated a top-10 player for the first time since January and will now feature in his second Masters Series semi-final of the year.
He takes on Djokovic, who hammered Swiss Stanislas Wawrinka 6-1 6-4, for the first time since the 2012 ATP World Tour Finals.
World number seven Federer has a 16-13 record against the Serb who won their last meeting in London a year ago.
"Roger is probably experiencing the worst season he's had in the last 10 years but he's still a player to beat in every tournament because he's Roger Federer, because he's won 17 grand slams," Djokovic told a news conference.
"You can't underestimate him although maybe he's not at the form where he was when he was number one in the world. But I watched his matches in Basel last week and here too and I think he's playing really well."
SEVENTEEN WINNERS
Federer showed his class in the first set of the quarter-final against Del Potro, clubbing 17 winners.
The Swiss was less sharp in the middle set and Del Potro, who did not have a single break chance until the 10th game of the second set, forced Federer into a decider.
Cheered on by a packed crowd, 2011 champion Federer then started to play more aggressively and broke serve in the seventh game.
"I think I did well to start stronger in the third set," he said. "That was something I couldn't quite do in Basel.
"Overall I was just hitting a better ball today and moving well and making good decisions time and time again. I was very happy with my level of play."
Djokovic, the 2009 champion, sprinted into a 3-0 lead against Wawrinka.
He never loosened his grip and left the seventh-seeded Swiss with the feeling he had little chance of victory.
"When he plays that good it's very difficult especially on this surface where he's the best I believe," Wawrinka said.
Ninth seed Gasquet probably felt much the same about Nadal, a player the Frenchman has yet to beat.
Gasquet, who will feature in next week's Tour Finals for the first time since 2007, tried to control the net as often as possible to compensate for his lack of power but made too many mistakes and easily surrendered despite the home crowd's support.
(Editing by Tony Jimenez)
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