The world No. 1 great secured his fourth title here in five years by handling the sixth-seeded Murray 7-6 (7-5), 6-7 (4-7), 6-3, 6-0 in 3 hours, 39 minutes at Rod Laver Arena.
It marked Djokovic's eighth career Grand Slam title in 15 major finals. He's also the reigning Wimbledon champ.
The great Djokovic also joined Stefan Edberg and Roger Federer as the only men in the Open Era to play in five finals at the Aussie Open. He has won all five of his finals here, including three now against Andy Murray, who also gave way to the Serb in the 2011 and 2013 finals, as well as an Aussie semi in 2012.
Djokovic and Murray are the only pair in the Open Era to contest three Aussie Open finals.
Djokovic snuck out the ultra-tight opening set via tiebreak before Murray returned the favor in the second. The match then took a turn for Djokovic in the third.
He broke Murray to even the third at 2-all, consolidated the break with a hold, and then managed to cruise from there.
The Serbian stalwart won 11 of the final 12 games, including nine in a row to seal the deal in Melbourne. The match came to a close when Murray netted one final backhand on Sunday night.
Capturing his first Grand Slam title since becoming a father, Djokovic said: "It's slightly different thinking for me now since I became a father and a husband."
A protester was stopped on court by security during the second set, causing a brief delay in play.
Tournament organizers said two people were arrested by police.
"Security responded immediately. Both were quickly removed with minimal disruption to play," organizers said in a statement.
Security guards caught one court invader, who was wearing a white shirt with the message "Australia Open for Refugees," near the baseline during a changeover after the seventh game of the second set. The players were surrounded by security staff while stadium officials took action.
A group of other people who had unfurled a large banner with the same message was escorted out of Laver Arena.
Djokovic improved to 16-8 lifetime against his fellow 27-year-old Murray, including 5-2 at Grand Slam events, and the Serb is now 3-2 in their career Grand Slam finals.
Djokovic is also now 5-2 versus Murray in best-of-five-set matches.
Murray had been 5-4 against Djokovic in their overall career finals matchups prior to Sunday.
Murray said the Aussie has been "the most consistent major of my career, but I just haven't been able to win it."
Djokovic improved to 49-22 in his overall career finals, while Murray dropped to 31-15, including 2-6 at the majors.
Djokovic now owns 50 career match wins at the Aussie, where only Federer (75-12) and Edberg (56-10) have secured more victories at this hardcourt major in the Open Era.
The amazing Djokovic has won his last 10 matches against fellow Top-10 players.
Djokovic claimed a first-place check worth just over $2.4 million, while Murray settled for $1.2 million as the bridesmaid.