Murray, who won the tournament in 2008 and 2009, now has 28 consecutive victories in ATP Tour matches.
Djokovic took a nasty fall in the next game, but with the help of two double faults from Murray, broke serve easily to go into the lead. The Serb then took the lead on return with an overhead victor but a return long leveled the pair up, and Murray came through the game with the hold.
The Scot has never beaten the Serb after losing the first set and he was soon trailing as Djokovic broke in the eighth game following a string of unforced errors from Murray. But with a match that ran so close, Murray shouldn't feel disappointed. His first serve worked like a charm and he was very aggressive, moving Andy around the court and making a lot of damage with his down the line shots from both wings.
Following three match points for Djok, Murray was showing all of his battling abilities to keep the match alive and eventually levelled things once more and a phenomenal inside-out, cross-court forehand victor.
The other quarter-final will pit third-seeded Tomas Berdych of the Czech Republic against fifth-seeded Jo-Wilfried Tsonga of France, who beat Dustin Brown of Germany 6-1, 6-3.
"I was a bit lucky to get through", said Murray. "So it was a big test for me today".
Djokovic is the defending champion in Melbourne, having won his sixth Australian Open title past year as he condemned Murray to a fifth defeat in the final of the tournament. While there was also action in Brisbane, Chennai and Perth last week, Doha is where world No1 Murray and No2 Djokovic committed to play. "The force of the nature is like that". Felt better each day. Djokovic more than doubled the top seed's victor output-13 to 5-collecting the first set in 49 minutes.
"I played a great match", said Nadal. The only thing, I am not sure about was my percentage of serves.
"I think he's playing much better than someone ranked 69 in the world", Murray added.
"It was a tough one to lose, but a great way to start the year". He's the World No. 3.
Too many mistakes from Murray took Djokovic through an easy hold of serve and a game away from the title. "You need to be ready for every single match". "I am going to try to make it happen, knowing that it's going to be an extremely hard match".
Raonic was aggressive in his match, but thought he should have attacked even more. "This is exactly what I hoped I can achieve".
"It's a great task", Raonic said.
Having covered the last seven-consecutive editions of the Qatar Open, I couldn't help but notice how more and more local kids are seen playing tennis on the outside courts on the sidelines of the event.