The world number one, who knocked out nine-time champion Rafael Nadal in the quarter-finals, goes on to face eighth-seeded Swiss Stan Wawrinka in Sunday's title match.
After their thrilling semi-final was halted due to a storm at 3-3 in the fourth set on Friday, Murray levelled the contest at two sets apiece.
But the Serb rallied in the decider to wrap up his eighth successive win over his fellow 28-year-old who he had also beaten in January's Australian Open final.
Victory on Sunday would make Djokovic only the eighth man to win all four majors and put him halfway to a rare calendar Grand Slam, a feat achieved by just two men, most recently by Australian great Rod Laver back in 1969.
"This is one of the toughest matches we have had ones we had, no doubt about that," said Djokovic who took his 2015 record to 41 wins against just two defeats, stretching his current streak to 28.
"Five sets over four hours. It's always physical. It's always demanding from every aspect of the game because we have similar styles of play.
"We tend to run each other around and play cat and mouse game, and it's tiring. It's exhausting to play him."
Sunday will be eight-time major winner Djokovic's 16th Grand Slam final and he will start as overwhelming favourite having beaten Wawrinka 17 times in 20 meetings.
For Murray, it was a third semi-final loss at Roland Garros meaning Britain's wait for a first men's finalist since Bunny Austin in 1937 goes on.
Djokovic had swept through the first two sets on Friday without facing a break point. But Murray conjured up a momentum-switching performance in the third set to haul himself back into the match.
That sent Djokovic off court for a lengthy medical timeout and just six more games were possible before the gloom and an approaching storm sent the players back to their hotels for the night after 3 hours and eight minutes on court.