ATP World Tour Finals
Venue: O2 Arena, London Date: 22-29 November
Tournament coverage: Live on BBC Two, 28/29 November, 1430 GMT; every match live on BBC Radio 5 live/5 live sports extra; live text commentaries on BBC Sport website; live coverage every day on Sky Sports
Djokovic was never at his best against a struggling Nadal at the O2 Arena
By Piers Newbery
BBC Sport at the O2 Arena
Novak Djokovic's reign as end-of-season champion ended on Friday despite victory over Rafael Nadal in his final round-robin match at the ATP World Tour Finals.
The Serb just about overcame the exhaustion he has talked about to win 7-6 (7-1) 6-3 in the afternoon session, but Nikolay Davydenko's 7-6 (7-4) 4-6 6-3 defeat of Robin Soderling in the evening saw both the Russian and the Swede qualify.
Nadal's hopes of reaching the semi-finals had already disappeared with defeats in both his opening matches, and he struggled with a back problem as Djokovic proved too strong in one hour 57 minutes.
Davydenko will play Roger Federer in Saturday's first semi-final at 1415 GMT, with Soderling taking on Juan Martin del Potro at 2045 GMT.
The qualification scenario was considerably clearer going into Friday's matches than it had been 24 hours earlier.
Day five had ended in chaos as Juan Martin del Potro was left waiting on court after beating Roger Federer to learn whether he had qualified, the Argentine eventually discovering that he had edged out Andy Murray by one game.
Djokovic simply knew that he must beat Nadal on Friday afternoon to stand any chance of retaining his title.
However, the 22-year-old Serb had looked desperately tired in his previous defeat by Davydenko while Nadal remained insistent that he was fully motivated despite a poor week.
Djokovic's apparent lack of motivation and Nadal's 14-6 head-to-head record in meetings between the pair also suggested the world number two might have the edge, despite the Serb comfortably winning when they last met in Paris two weeks ago.
But Nadal has struggled for form and looked underpowered since returning to the tour following the knee and abdominal injuries that disrupted his year.
It was therefore no surprise that the 21st meeting between the world numbers two and three produced arguably the lowest quality tennis of any of those matches.
The first three games went against serve and Nadal looked like making it four when he earned another break point, but the Spaniard missed with his return and Djokovic - with the help of a fabulous lob - held to lead 3-1.
Djokovic was marginally the more consistent in the baseline exchanges as Nadal struggled on his usually fearsome forehand in particular, but it was hardly vintage stuff from the champion and a backhand into the net brought Nadal level at 4-4.
It may not have been the greatest tennis ever but the 17,000 spectators in the O2 Arena were thrilled to see two of the world's best at least locked in a tight battle.
Nadal received treatment for a back injury during the second set
And the tie-break that followed provided plenty of excitement, with a couple of leaked forehands the early difference as Nadal slipped 4-2 down.
A superb lob volley helped Djokovic to 6-2 and four set points, and despite seeing three of them disappear, the Serb converted the fourth when Nadal mishit a forehand.
The two players had managed a disappointing 43 unforced errors between them in the first set, and there were fears that the end might be in sight when Nadal required a medical timeout for attention to his lower back at 2-1 down in the second.
The Spaniard returned to the action but immediately dropped his serve with a forehand into the middle of the net, and staved off another break point in game six.
There was little sign of Djokovic being derailed until he served for victory and, despite his body language suggesting otherwise, the Serb had sufficient energy to recover from 0-30, save a break point and close out the win on his third match point.
After the match, Djokovic admitted he was running on empty.
"I'm not saying I'm dead tired, I'm saying I'm exhausted from the season," he said.
"And I think you don't need confirmation from my face to see that. I think it's obvious on the court that I'm not moving and I'm not that energetic as I was maybe in Paris or Basel.
"Still, I managed to get two out of three wins. If I finish the season now, I will be very happy to finish in this way and just hope to rest well for 2010."
"It was a match that I didn't play for a lot, I just tried to finish without bad feelings, and I think I did for moments," said Nadal, who confirmed that he had felt his lower back when serving at 1-1 but played it down.
Asked how he felt about losing all three matches, Nadal added: "It's disappointing if you arrive here with the feeling that you have a big chance to win, but I didn't arrive here with that feeling.
"I knew before the tournament that it was going to be really tough, difficult, but I tried. Every day I tried my best, nobody can say I didn't. But that's tennis. I'm playing against the best players in the world - it wasn't enough on this surface."
Seventh seeds Max Mirnyi and Andy Ram earlier beat fourth seeds Lukas Dlouhy and Leander Paes 7-6 (7-1) 6-4 to qualify for the last four from doubles Group B.