Murray became Britain's first major champion since Fred Perry claimed his third American title in 1936, the year the Spanish Civil War started and Franklin D Roosevelt was re-elected US president.
In a roller-coaster final, which witnessed a 54-shot rally, numerous 30-stroke exchanges, as well as a record-setting tie-breaker, the 25-year-old Murray held his nerve in a knife-edge final set.
The Olympic champion led 3-0 in the decider, dropped serve but broke again for 5-2 when Djokovic called a medical time-out.
But Murray wasn't to be denied, taking the historic crown when Djokovic went long with a forehand on a second match point in what was, at four hours and 54 minutes, the second-longest US Open final of all time.
Murray insisted it was a huge relief to finally have captured a major and put an end to the questions over whether or not he would do it.
"Most press conferences I would do I would get asked a question along those sort of lines, and it does build pressure a little bit," he said.
"You try not to think about it much when you're playing, but when I was serving for the match, I realised how important that moment was for British tennis. It's something that hasn't happened for a long time."
"And, yeah, I'm obviously proud that I managed to achieve it and don't have to get asked that stupid question again."
Murray paid tribute to coach Ivan Lendl, who lost three finals in New York from 1982-1984 before clinching three titles in a row from 1985-1987.
"He was one of the greatest," Murray said. "He has helped me through the tough times."
Djokovic admitted Murray was a worthy winner.
"Any loss is a bad loss. I'm disappointed to lose the match, but in the back of my mind I knew that I gave it all. I really, really tried to fight my way back through," said Djokovic.
"I had a great opponent today. He deserved to win this Grand Slam more than anybody because over the years he's been a top player. He's been so close; lost four finals. Now he has won it, so I would like to congratulate him."