Murray came under pressure early in the first set as the world number one made him face break points in his opening service game, but the Briton held serve.
The Scot served to take the opener to a tie-break, but his first double fault of the match gave his opponent two set points, and he clinched the second when Murray sliced the ball into the net.
It looked like Djokovic would cruise to the win early in the second when he had three break points, but Murray dug deep to hold, before going a break up himself in the next game.
The top seed struck back straight away though before taking a break of his own, leaving Murray to serve to stay in the match at 5-2 down.
Murray battled to try to keep himself in the match, but a string of unforced errors gave Djokovic match point, which he secured when the British player failed to clear the net with a backhand.