Murray had clawed back the third set before play was suspended on Friday night at 3-3 in the fourth and the British number one picked up where he left off on Saturday to force a dramatic decider.
Djokovic, however, was relentless in the fifth, breaking twice to seal a 6-3 6-3 5-7 5-7 6-1 victory and the Serb will now play Switzerland’s Stan Wawrinka in Sunday’s final.
“It was a very difficult match,” Djokovic said. “I started well early on with good aggression and intensity but Andy found his confidence on the court.
“The first game of the fifth set was very important and after that I started to play much better.”
Djokovic had not dropped a set at Roland Garros when he took to Court Philippe Chatrier on Friday and he looked certain to extend that record when he raced into a two-set lead.
Murray, however, turned the tide at 5-5 in the third, producing two scintillating points to break, before sealing the set and sparking hopes of a comeback.
Djokovic took a medical time-out, perhaps to kill his opponent’s momentum, but Murray’s march could not be halted and, with the crowd behind him, he broke again before Djokovic responded to put the match on serve when the umpire called time for bad light.
Both players were desperate for a strong start when play resumed on Saturday and neither could be disappointed as four games rushed by with only one point earned against serve.
Djokovic showed few signs of nerves as he blasted away into the corners but at 5-5, a superb Murray drop-shot was too cute and the Scot converted the second of two break points to lead 6-5.
It was a dream start for the British number one and he kept his composure to serve out as a Djokovic backhand flew long to send the contest to a decider.
The emotional energy expended on sealing the set perhaps diverted Murray’s focus because the Scot’s faultless hitting suddenly went awry in the second game of the fifth when four unforced errors gifted Djokovic a break.
Murray had pushed his opponent to the limit but now Djokovic was in charge, dictating the points with unrelenting accuracy and in the sixth game he broke again to serve for the match at 5-1.
It was the eight-time grand slam champion at his very best and Murray was helpless to prevent his opponent sealing a stunning victory, which he did with an ace, after a two-day battle lasting four hours and nine minutes.