After losing the first set to the British number one on Philippe Chatrier, Djokovic cut a dominant figure against a game but ultimately drained and valiant Murray, almost breaking serve at will against an opponent who appeared to run out of steam having won the first set in some style.
More importantly for Djokovic, 29, in winning his 12th Grand Slam, the Serbian undisputed world number one becomes only the third man in history to hold all four majors at the same time.
"It's a very special moment, possibly the biggest moment in my career," the 29-year-old said courtside.
After two final defeats to Rafael Nadal and last year's loss to Stanislas Wawrinka, the game's outstanding player has finally clasped the tournament that threatened to elude him.
He is suddenly firmly in the discussion when it comes to debating who is the greatest in the sport’s history with Roger Federer’s total of 17 looking increasingly under threat.
Don Budge in 1938 and Rod Laver in 1962 and 1969, watching this week, are the only other men to hold all four slams of the Australian Open, French Open, Wimbledon and the US Open at the same time.
He could yet make his astonishing feat a calendar Grand Slam if he can defend his titles at Wimbledon, which begins later this month, and the US Open in September.
It was another tough afternoon of schooling for the flying Scot Murray who remains the game’s second best player, but some way behind Djokovic, who leads him 24-10 in career head-to-heads and 5-2 in Grand Slam finals.
Murray last tasted victory over Djokovic in a Grand Slam final when he lifted the Wimbledon title in 2013.
Murray has fallen to defeat eight times in 10 Grand Slam finals despite being the first British man to reach the Roland Garros final since Bunny Austin in 1937, two years after Fred Perry was champion in 1935.
Yet it all began so well for the Dunblane player, who, after being broken to love in the opening game of the match, roared back with four straight games to sting the top seed in taking the opening set in just under an hour.
From then on the French crowd were treated to a Djokovic masterclass.
He recovered strongly to win the second set 6-1 in levelling the final at one set all, and his dominance continued in the third set after breaking an increasingly exhausted-looking Murray, who was suddenly faced with the task of winning the final two sets to keep alive his hopes of a first French Open success.
With Murray’s serve continuing to falter badly, Djokovic seemed to have applied the final dagger when he broke to love in the seventh game of the fourth set for a 5-2 lead with two breaks.
He broke into a huge smile but the final was not over as Murray somehow rallied again by breaking before holding to force Djokovic to serve out for his place in history.
He duly did despite Murray, blessed with a terrific attitude if not quite the technique of the man on the other side of the net, saving two match points before finally succumbing to the delight of a largely pro-Djokovic crowd.
"This is his (Djokovic) day today. What he has achieved the last 12 months in phenomenal, winning all four slams in the same year is an amazing achievement." Murray said in his post-match press conference.
Read the original article on Eurosport: Djokovic seals career Grand Slam by outclassing Murray to win maiden French Open title