The top-ranked Murray barely kept alive his dream of finishing the year at No. 1, needing more than 3 1/2 hours to dispatch fourth-seeded Milos Raonic of Canada 5-7, 7-6 (5), 7-6 (9) in Saturday's first semifinal.
It was the second marathon victory of the week for Murray, who extended his match winning streak to 23. The top seed from Great Britain beat Japan's Kei Nishikori in a 3-hour, 21-minute match on Wednesday -- previously the longest in tournament history.
"I'm tired. I've played so much tennis over the last few months," Murray said after dispatching Raonic. "I'll give it my best effort -- the best of what I have."
Djokovic, who had his 122-week reign at No. 1 halted by Murray earlier this month at the Paris Masters, breezed into the finals by overpowering Nishikori 6-1, 6-1.
A five-time champion at this event, Djokovic steamrolled Nishikori in only 66 minutes in the Serbian's bid to wind up No. 1 for the third consecutive year and fifth time overall.
Sunday's encounter between Murray and Djokovic will mark the first time that the No. 1 ranking has been on the line in the championship match of the season finale.
"This has never happened in the history of tennis," Djokovic said. "I'm privileged to be part of the history. This is one of the biggest matches we will ever play against each other."
World No. 2 Djokovic has a decided edge in the series history against Murray, winning 24 of their 34 career matches.
Djokovic has won three of the four meetings against Murray this year, claiming Grand Slam titles at the Australian Open and French Open at the Scot's expense. Djokovic also prevailed in the finals of the ATP World Tour Masters 1000 event in Madrid, while Murray beat Djokovic for the title in Rome.