The 32-year-old's 6-3 6-3 defeat of Khachanov was his 15th successive singles win in the competition and he was soon back out on court with Troicki.
The game was tense and even, with Djokovic suffering physical problems in one elbow and stopping the game on occasion to receive medical attention.
The 20-time Grand Slam victor recovered from a shaky start to came out on top 3-6, 6-4, 6-2 versus the lanky German.
The British pair had set points to take it to a decider, but Spain, and Nadal in particular with one sublime overhead after a brilliant reach, produced their best when the pressure was at its greatest. "That's it. The season is done and we're turning the next page".
"Both teams had a lot of chances", said Rublev, who won the opening singles against Filip Krajinovic 6-1, 6-2.
Russian Federation pulled off a 2-1 upset over Serbia on Friday in Madrid to reach the semifinals of the Davis Cup for the first time since 2008 thanks to a victory in doubles by Karen Khachanov and Andrey Rublev.
"As I run around the whole time and I use them for running but then of course I also may explore the idea of a tennis shoe, we will see what is going to happen there". In his absence, Kyle Edmund beat Philipp Kohlschreiber 6-3, 7-5 in the first rubber with Daniel Evans taking three sets to see off Jan-Lennard Struff 7-6 (8/6), 3-6, 7-6 (7/2).
"There are some very nice quotes and I'm happy I played against some of them", Federer said.
"It was absolutely insane", Federer said of the tour.
But poor turnouts for some of the group-stage ties, particularly in the morning sessions, have been a major concern while other problems, including painfully late finishes, mean there is room for improvement.
The last doubles rubber between Italy and the US finished at 4.04am local time on Thursday, prompting both morning and evening sessions to be brought forward by half an hour.
The Russians are in the semis for the first time since 2008 and will have to do it all over again on Saturday when they face Canada who enjoyed a rest day after beating Australia on Thursday.
"I am going to be working also beyond my playing days, which I was anyways always going to do - also with my charity and then I have my four children and my wife and I want to spend maximum time there".
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