But Murray turned the tables in the semi-finals at the Olympics and then beat Djokovic to win his first Grand Slam title at the US Open last September.
Born a week apart, they played each other as juniors and have matched each other almost step for step in the men's game, so, in truth, there is little they don't know about each other's game.
But if there is one man who might be able to find a chink in the world No 1's armour, then perhaps it is Murray's coach Ivan Lendl, who is beginning his second year in the job.
Lendl's influence was instrumental in Murray's triumph in New York and the former world No 1 may have a couple of tricks up his sleeve should the two men meet again in the final in Melbourne.
"I watched the second and fifth set of last year's semi-final with Novak here," Lendl said yesterday, confirming he sometimes watches videos to gain an insight into the Scot's opponent. "It was interesting. I picked up things, but I'm not going to tell you what they are."
Few men in the sport keep their cards closer to their chest than Lendl, who is notoriously careful not to give away any information that could help any of his charge's rivals, either now or in the future.
The eight-times Grand Slam champion has helped Murray shed the self-doubt he admitted had caused him to question whether he had what it took to win one of the sport's major prizes, at the same time forging a growing reputation for himself as an insightful coach. In their final at the US Open, Murray won countless big points by serving out wide to the Djokovic forehand from the deuce court. The Serb has very few weaknesses but Murray, with the help of Lendl, found them.
It would be churlish in the extreme to write off Roger Federer as a threat at these events, especially since he beat Murray in the Wimbledon final last summer to deny the Scot glory on his home turf. But it is three years since he reached a Grand Slam final on hard courts, when he beat Murray to win the Australian title here, and his results since then have not been as exceptional as in the golden years when he was at his peak.
The 17-times major champion also goes into the tournament having not played a single competitive match since the World Tour Finals in November and with Rafa Nadal out through injury since Wimbledon, the sneaking suspicion is that Djokovic and Murray may be about to forge a new rivalry at the top.
"It is a definitely a possibility," Lendl said. "There are a lot of factors that affect it: health, somebody else coming up, Roger staying around, Rafa coming back – all those things. But yes, it is a possibility. I could see it happening. I am not saying it is going to happen, but I can see it happening."
It is just over a year now since Murray announced, to the surprise of most in tennis, that the Czech-born Lendl would be his new coach, despite having no experience in coaching at the top level.
But the two men, their natures not dissimilar, gelled immediately and Lendl, who, like Murray, lost his first four Grand Slam finals, said he was most pleased with his attitude and ability to take advice.
"He kept working hard throughout the year, but we knew he was a hard worker," Lendl said. "Maybe even more, because of the honesty I came in with, I can say things and he takes it well. Because at times, it could be difficult. However, you can get through things much quicker if you are honest with each other and I like to operate that way."
Murray made the perfect start to the year by winning the title in Brisbane, as he did 12 months ago, and Lendl said if he had one wish, it would be simply that his charge keeps winning.
"Ideally, I would like to see him lose fewer matches," Lendl said, with a straight face. "Zero would be a great number though we all know that is unlikely to happen. Winning and winning obviously breeds confidence and confidence breeds more winning and that is why I was very pleased with last week in Brisbane. Even though it is a relatively small event, it is always good to win and it helps."
Murray begins his title bid against Dutchman Robin Haase on Tuesday and Lendl said he would consult with Murray's other coach Dani Vallverdu before formulating a game plan for a man who beat Murray once and pushed him close at the US Open in 2011.
Lendle admitted: "I don't have much on Robin Haase even though I did watch him one match in Barcelona because he was set to play Andy and then lost. So I'm going to rely more on Dani for this one. The way it works is the three of us sit down, I ask everybody what they think and we go from there. If there is something I think more or differently, we go from there and that's how we do it."