The defending champion, who said he had breathing problems in his quarter-final against David Ferrer, looked tired throughout the match but still managed to win 6-3 3-6 6-7 6-1 7-5 in four hours, 50 minutes and deny Murray a third successive Melbourne Park final.
"It's difficult to describe. I was trying to focus on every point," Djokovic, who meets Rafa Nadal in Sunday's final, said in a courtside interview.
"It was a physical match. It was almost five hours. It was one of the best matches I played. Emotionally and mentally it was hard.
"We were always trying to hold our serves. It felt like we were breaking each other easier than serving it out.
"Andy deserved the credit to come back into the match ... Thank you guys for staying this late and hopefully be entertained."
Image: Novak Djokovic of Serbia celebrates after defeating Andy Murray of Britain during their semifinal at the Australian Open tennis championship, in Melbourne, Australia, early Saturday, Jan. 28, 2012.
Australian Open 2012