"I want to talk about how well he played all week", said Djokovic.
Khachanov, the victor at last month's Kremlin Cup in Moscow, will meet either defending champion Jack Sock or Austrian sixth seed Dominic Thiem for a place in the final.
After beating John Isner in a marathon match on Tuesday, the Russian took rather less time to down Zverev 6-1 6-2, with the German appearing to take offence to some of Khachanov's team as they reacted to an error.
Khachanov, who won the Kremlin Cup in Moscow last month, broke fourth-seeded Alexander Zverev's serve six times in a 6-1, 6-2 win.
Novak Djokovic overcame nagging flu and a formidable examination from Marin Cilic, having to come from a set down to forge into the Paris Masters semi-finals with racket-smashing intensity and extend his winning streak to 21 matches on Friday.
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Between them they have 59 Masters titles and 34 Grand Slams.
Brilliant one-handed winners on the run from Federer down the line and acute-angle volleys at the net; astonishing elasticity while retrieving from the baseline and laser-beam forehands to the corners from Djokovic.
Djokovic briefly let his volatile temper get the better of him, though, when he had Federer at 15-40 down in the ninth game of the deciding set. "But it's not easy to perform every single day, the energy levels are not as high", he told reporters on Friday.
Djokovic, who is guaranteed to take the No. 1 ranking on Monday, struggled on his serve for much of the first set.
The players swapped breaks at the start of the second set before Khachanov reeled off the next five games, clinching victory on his first match point when the sixth-seeded Thiem chopped a shot wide.
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The best one of the match went to Federer in the eighth game. From a seemingly impossible angle, and totally off balance, he scooped his racket behind his neck and flicked a volley over the net for a victor.
Even by Federer's lofty standards, it was remarkable.
But after losing the match, Federer was left shaking his head. "Somehow a lot of breaks are happening", Thiem said.
"Thank God the rally ended", he said.
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