Djokovic, who is chasing a sixth title at the season-ending championship to match Roger Federer's record, drew first blood in a tight opening set to take a 5-3 lead and consolidated the break for the early advantage in the match.
Trailing 5-4 in the next, the Serbian saved three set points and drew level with a blistering cross-court shot at the end of a 26-shot rally but appeared to struggle physically in losing the tiebreak as he allowed Medvedev back into the match.
Having already reached the semi-finals after beating Andrey Rublev (25) on Wednesday, some might have expected Djokovic to ease up and save his energy for Saturday's semi-final meeting with Taylor Fritz (25) but he responded in style.
The Serbian battled back from a break down in the decider to hand Medvedev his third straight defeat after three hours and five minutes.
"Daniil and I have had some battles in the past and I knew coming into the match it was going to be his last of the season and he wouldn't want to finish with a loss," Djokovic said.
"I started off well, had chances in the second set, had break points but he played very well in those decisive points. He was playing really quick. I didn't feel physically well in the third, struggled a lot. It's a battle and it's a fight.
"Being able to find the last drop of energy to come back ... at 4-5 (in the third set) I managed to read his serve and anticipate well and got myself in a good position."
Greek Stefanos Tsitsipas (24) meets Russian Rublev later on Friday, with the winner facing Norway's Casper Ruud (23) in the semis.
