The Scotsman, beaten in his four previous grand slam finals, made it fifth time lucky with a nerve-jangling 7-6 7-5 2-6 3-6 6-2 victory at a windy Arthur Ashe Stadium where the players had to battle the elements as much as each other.
With both men struggling to control the ball in the gusting winds, and battling exhaustion in a final that tied the record as the longest at Flushing Meadows, the match became a test of courage and stamina and it was Murray who handled the decisive moments better.
After losing the first two sets, Djokovic suddenly raised his game to win the next two and force a deciding fifth set, seizing the momentum as Murray started to wilt.
But the Olympic champion regained his composure and jumped out to a 3-0 lead in the final set with two service breaks then hung on to seal an emotional victory.
"It was incredibly tricky conditions. After the third and fourth sets it was tough mentally for me," said Murray.
"Novak is so strong. I don't know how I was able to come through in the end."
The 25-year-old Murray, a survivor of the 1996 Dunblane school massacre, won a titanic first set that took almost an hour and a-half to complete and ended in a 22-point tiebreaker, then added the second set despite blowing a 4-0 lead against the defending champion.
Djokovic, already a five-time grand slam champion, rebounded to win the third, then the fourth to raise the prospect that he could become the first man to win the final after losing the first two sets since Pancho Gonzales in 1949.
However, the world number two was unable to conjure another fightback as his legs started to cramp and Murray wrapped up victory after four hours and 54 minutes, the same time it took Mats Wilander to beat Murray's coach Ivan Lendl in the 1988 final.
"It wasn't to be but I want to congratulate Andy for his first grand slam, he absolutely deserves it," Djokovic said.
The last British man to win a grand slam was Fred Perry, who clinched his final major in New York in 1936 when men played tennis in long trousers and used wooden racquets.
It was the same year Britain's King Edward VIII abdicated to marry American socialite Wallis Simpson.
Murray emerged as the man most likely to end that barren run when he made it to the 2008 US Open final, losing to Roger Federer in straight sets. He then made the Australian Open final in 2010 and again in 2011 but doubts about his mental toughness grew when he lost them both in straight sets.
The turning point came just a few months ago.
He made the final at Wimbledon and although he lost to Federer he won the first set and with a bit of luck, might have won the match.
A few weeks later, he avenged his loss to Federer by beating him in the Olympic final.
