“I was super lucky,” a relieved Nadal said. “Daniil is a tough player and was was playing much better than me today.
Nadal claimed victory as a Medvedev backhand which looked to have kissed the sideline was determined out by electronic linecalling.
The Russian claimed the opener with seven aces and never faced a break point as he put the top seed into difficulty.
Along the way, the veteran saved a match point at 5-1 as the massive momentum shift materialised .
After the match Nadal was loathe to put any special emphasis on his fightback from 5-1 down in the third set which evolved into a 6-7(3), 6-3, 7-6(4) defeat of Daniil Medvedev.
Nadal, who had saved a match point along the way against the Russian whom he beat in the US Open final in September, insisted there was nothing special about his performance.
In fact, he could barely rate the epic which went for almost three hours.
“It was not one of the best performance of my career, I really hope that I can play better,” the 19-time Grand Slam champion said.
“But it was better than the other day (loss to Alexander Zverev in group play)
Winning this match was a combination of a lot of things: lucky, some mistakes of Daniil, some good moments for myself at the end.”
Nadal said that the abdominal muscle injury which forced him to quit the Paris Masters has not been a problem, with his fitness improving by the day here with one final round-robin match to go on Friday.
“Only being able to increase the practice level only two days ago, this is a very positive thing,” he said..
“I’m very happy with this (improvement). Win or lose is another story.”
The 33-year-old who has never won a year-end titleadmitted that he had not been counting on pulling off a miracle on court.
“In that moment (facing a Medvedev match point, which he saved), you think in five minutes you are in the locker room, that’s the normal thing.
“You are not playing with much pressure because you have almost lost.
“I played a great point and then I was able to save that game. Even with 5-2 is so difficult to think about comeback against a player like Daniil, especially indoors.
“On clay, you have more chances because normally you play more points. But here, you are in his hands.”
Nadal said he started to entertain upset thoughts trailing 5-3.
“Being only one break away, why not? I need to create the moment and I need to put the pressure.
“I played a good game and then he made a couple of mistakes, then I played a good tiebreak.”
Later Stefanos Tsitsipas joined Dominic Thiem in the London semis after defeating holder Alexander Zverev 6-3, 6-2.
The victory in 75 minutes narrows the possibilities for the remaining pair of places in the final four for the Saturday start of the knockout stage.
Against his German opponent, Tsitsipas sent over eight aces and broke three times.
The win by Tsitsipas was his third this season against Zverev, with the other victories coming in Madrid and Beijing.