Murray will face world number two Djokovic or Japan's Kei Nishikori in Sunday's final.
Andy Murray remains on course for a dramatic showdown with Novak Djokovic as the world number one staged a superb fightback to defeat Milos Raonic 5-7, 7-6 (7/5), 7-6 (11/9) in the semi-finals of the ATP Tour Finals on Saturday.
Murray will face world number two Djokovic or Japan's Kei Nishikori in Sunday's final after surviving a three-hour 39-minute classic that ranked as the longest match in Tour Finals history.
The Scot, who saved a match point in the final-set tie-break, must win the Tour Finals for the first time to be guaranteed to finish 2016 on top of the world rankings, with Djokovic able to overhaul him if he takes the title for a record-equalling sixth time.
Murray would also finish number one if Djokovic loses to Nishikori later on Saturday.
If Djokovic does make the final, he might find Murray running low on energy after the Wimbledon champion was pushed to his limits by Raonic just days after he had endured the previous longest match in the tournament, a victory over Nishikori that took three hours and 20 minutes.
"It was obviously unbelievably tough. I played some great points and managed to get the break at the end," Murray said.
"It was an amazing atmosphere. The longer the match went on the louder the crowd got. This is what we play for -- matches like this and arenas like this.
"This is one of the hardest matches I've played indoors. I didn't expect to play a long one with someone with a serve like Milos.
"I'm tired. I've played so much tennis over the last few months. I'll give it my best effort, the best of what I have."
Raonic twice broke Murray when he served for the match in the final set and saved three match points in the decisive tie-break.
But the Canadian fourth seed couldn't take the one match point that came his way in a thrilling denouement that eventually went Murray's way to repeat the outcome of their meetings in the Wimbledon and Queen's finals on the other side of London earlier this year.
Murray's 23rd successive victory set a new career-best for the 29-year-old but only a 24th would bring a fitting finale to the best year of his life.
Having effectively handed Murray the number one ranking by withdrawing ahead of their semi-final in Paris two weeks ago, Raonic now had the chance to deal a hammer blow to the Scot's hopes of keeping it.
Murray saved a break point in the third game of the first set and then three more at 4-4.
His resistance cracked two games later as a tired double fault gave Raonic the chance to serve for the set, which he took on his third set point.
When Murray dumped a forehand into the net to give Raonic a break in the third game of the second set, he looked in deep trouble.
His recovery was less down to his own brilliance than a lapse from Raonic, who immediately played a dreadful game and was broken to love.
Murray saw a 4-1 lead dragged back to 5-5 in the tie-break, but he held his nerve to level the match.
In an incredible finish, Murray was on the cusp of victory when he broke for 5-4 and 6-5 leads in the final set.
But on both occasions Raonic responded superbly to force the thrilling tie-break that once again showcased Murray's steely determination as he dragged himself over the finish line.