The top-ranked Djokovic faced only three break points in the match, saving them all, and lifted his tempo when it counted most.
His five-set, 5-hour, 53-minute win over Rafael Nadal in the 2012 final is already part of Australian Open folklore. He tore off his shirt and flexed his muscles after the marathon win last year, and is hoping to add another chapter by becoming the first man to win three consecutive Australian titles in the Open era.
Nine others have won back-to-back titles — none have had three in a row since the Open era started in 1968.
"Hello everybody it's great to be back," Djokovic told the crowd. "I have great memories, especially the last two years."
Djokovic lost a match to Australia's Bernard Tomic in the exhibition mixed team Hopman Cup tournament earlier this month, but brushed that off as a way to combine "fun and some great matches" as preparation for the major.
On Monday, he hit 31 winners against only 15 unforced errors.
Maria Sharapova and Venus Williams had nearly flawless opening matches in the women's draw earlier in the day.
Sharapova finished her first match of the year in 55 minutes, cruising to a 6-0, 6-0 win over Olga Puchkova to start proceedings on center court without showing any signs of trouble with her sore right collarbone.
The No. 2-ranked Sharapova, who lost the final to Victoria Azarenka here last year before going on to win the French Open, faced only two break points in the match and she saved both of those in the first game.
Then she went on a 12-game roll that earned her a second "double bagel" inside a year.
Sharapova withdrew from the Brisbane International earlier this month with an injured right collarbone, saying she wanted to concentrate on being fit for Melbourne. She skipped the Brisbane tournament last year, as well, before going on to reach the Australian Open final.
"After a couple of close games and a few break points, I certainly started to concentrate a bit better," she said. "I didn't want to concentrate on the fact I hadn't played a lot of matches. I just wanted to focus on what was ahead of me and really be aggressive.
"It was one of those matches where I didn't try to worry about her too much."
Sharapova has a potential third-round match against Venus Williams, who needed just an hour for her opening 6-1, 6-0 win over Galina Voskoboeva of Kazakhstan.
No. 4 Agnieszka Radwanska won the last nine straight games in her opening 7-5, 6-0 win over Australian wild-card entry Bojana Bobusic 7-5, 6-0 and 2011 U.S. Open champion Samantha Stosur beat Chang Kai-chen of Taiwan 7-6 (3), 6-3 to end a run of five losses on home soil.
Sixth-seeded Li Na, who lost the Australian Open final before winning the 2011 French Open, had a 6-1, 6-3 win over Sesil Karatantcheva of Kazakhstan, while No. 18 Julia Gorges of Germany and No. 27 Sorana Cirstea of Romania also advanced. Former No. 1-ranked Jelena Jankovic beat Sweden's Johanna Larsson 6-2, 6-2.
On the men's side, 2010 Wimbledon finalist Tomas Berdych defeated Michael Russell 6-3, 7-5, 6-3, No. 10 Nicolas Almagro of Spain beat American qualifier Steve Johnson 7-5, 6-7 (4), 6-2, 6-7 (6), 6-2, No. 15 Stanislas Wawrinka beat German qualifier Cedrik-Marcel Stebe 6-2, 6-4, 6-3 and No. 16 Kei Nishikori of Japan had a 6-7 (5), 6-3, 6-1, 6-3 win over Romania's Victor Hanescu.
Also advancing were No. 26 Jurgen Melzer of Austria and No. 32 Julien Benneteau of France, who ousted rising Bulgarian star Grigor Dimitrov 6-4, 6-2, 6-4.
Venus Williams played with power and determination and took command of the match early with a steady stream of winners and powerful serves.
She skipped last year's Australian Open due to illness and was warmly welcomed with applause as she entered the court. Venus Williams had the biggest jump of any of the top players in 2012, moving from outside the top 100 to finish the year at No. 24.
The announcer told the crowd as Williams, who has won seven major titles, was warming up on court: "She's back and fiery."
Williams said she was happy with the match statistics, particularly her serve, so early in the season.
"It's hard to play the first match in a major, first thing of the year, and that can be a lot of pressure,' Williams said. "I did my best to just close it out."
Her younger sister, Serena, was sitting in the crowd with coach Patrick Mouratoglou. Serena is the strong favorite to win the Australian Open, heading into the tournament with 35 wins in her past 36 matches including titles at Wimbledon, the Olympics and the U.S. Open.
No. 3-ranked Serena Williams is in the top half of the draw with defending champion Victoria Azarenka, and the pair won't start until Tuesday.
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