Facing second-ranked Rafael Nadal in the final Sunday, he'll try to become only the fifth man since the Open Era started in 1968 to win three straight majors, joining Rod Laver, Pete Sampras, Roger Federer and Nadal.
"I'm extremely delighted to be in the final," Djokovic said. "What can be a bigger challenge than playing against Rafa Nadal, one of the greatest players ever."
Despite appearing tired and sore after the second set, Djokovic rallied to beat Murray in a rematch of the 2011 final at Melbourne Park to reach his third consecutive Grand Slam final.
After wasting a chance to serve out the match at 5-3 in the fifth and letting Murray back into the contest, Djokovic cashed in his first match point when the Scottish player missed a forehand after four hours, 50 minutes.
Djokovic dropped onto his back, fully laid out on the court. He got up and shook hands with Murray, before jogging back out onto the court like a boxer, dropping to his knees and crossing himself.
"You have to find strength in those moments and energy, and that keeps you going," he said. "At this level, very few points decide the winner.
"I think we both went through a physical crisis. You know, him at the fourth set, me all the way through the second and midway through the third. It was a very even match throughout, from the first to the last point."
It was already after 12:30 a.m. local time Saturday when he got up again and pumped his arms triumphantly.
"Andy deserves the credit to come back from 2-5 down. He was fighting. I was fighting," Djokovic said. "Not many words that can describe the feeling of the match.
"It was a physical match ... it was one of the best matches I played. Emotionally and mentally it was equally hard."
It was a bitter setback for Murray, who lost the previous two Australian finals.
Murray believes he's already improved in the few weeks since hiring eight-time major winner Ivan Lendl as coach.
"Yeah, it was tough at the end 'cause, you know, obviously you come back, then you get close to breaking," he said. "But a different player, a different attitude to this time last year. I'm proud of the way I fought."
Djokovic finished last year at No. 1 after winning three of the four majors, including a straight-sets win over Murray in the Australian final. His only loss at a Grand Slam in 2011 was against Federer in the French Open semifinals.
It was phenomenal season after previously only winning one major -- the 2008 Australian Open -- and not returning to a final for 11 Grand Slams.
"To be honest, I think I matured as a player. I started to believe on the court I could win majors," he said. "Rafa and Roger are the most dominant players for the last seven, eight years. ... It was very hard to take away the titles from them. They will not give you the titles. You have to earn it."
Djokovic's 70-6 win-loss record in 2011 included those six wins over Nadal in finals -- including Wimbledon and the U.S. Open. However, Nadal will have an extra day to prepare for this final.
In 2009, Nadal beat Fernando Verdasco in a 5-hour, 14-minute semifinal before facing Federer in the final and winning less than 24 hours later.
On Friday night, both Djokovic and Murray had form dips -- but Djokovic's were more obvious. He led by a set and a break before Murray started coming back. Then Djokovic started walking gingerly and appeared to be struggling for breath -- just as he had been in his straights sets quarterfinal win over No. 5-ranked David Ferrer.
At one point, he pointed to his nose and seemed to indicated to his support group that he was having trouble breathing.
In the opening game of the third set, Djokovic had to fend off five break points before holding a game that lasted 14 minutes, then asked the chair umpire for a handful of tissues to blow his nose.
He said his breathing problems were from allergies, and said he'd seen a doctor.
He stayed in the points, despite Murray scrambling and trying to get him involved in long rallies. Relentlessly pushing the limits hurt Murray in the end, finishing with 86 unforced errors against 47 winners. Djokovic had 69 unforced errors and 49 winners.
After winning a tight third-set tiebreaker but then virtually conceding the fourth set, Murray rallied again after falling behind 5-2 in the fifth. He broke Djokovic at love when the Serb was serving for the match and rallied to tie it 5-5, putting all the pressure back on the defending champion.
But Djokovic composed himself and seemed to gather energy as the match wore on. He held serve and then broke Murray to finish it off.
"I'm going to try to recover," Djokovic said. "Obviously, it's going to be physical as well."
Despite being friends and childhood rivals, this was only the second meeting between Djokovic and Murray at a Grand Slam. Djokovic beat Murray in the 2011 Australian final and had a 6-4 lead in their overall head-to-heads at tour level.
Murray won the Brisbane International and came into the semifinal on a 10-match winning streak with Lendl in his box.
The blue-and-white crossed Scottish flags fluttered in the crowd, held by fans with the flag painted on their faces and some wearing their tartan Tam hats. The support was evenly split at Rod Laver Arena, encouraging both players in the tense final set.