Monaco succumbed as much to injury as to Russian Andrey Kuznetsov in a 7-6 6-1 6-1 first-round defeat.
With all the seeds safely through to the second round as the shadows lengthened over show court two, the 28-year-old took lengthy injury time-outs for treatment on his lower back and hip in a desperate bid to keep the record intact.
The 11th seed was clearly struggling, however, and howled in frustration as the 21-year-old Kuznetsov took advantage of his opponent's restricted mobility to move to the brink of victory.
Monaco, who pulled out of the Kooyong Classic warm-up last week with a hand injury, won applause from the crowd for his spirit in not retiring.
"My leg tightened up at the start of the second set and it was very tough for me," he told Reuters, gesturing to his upper right leg.
"It was always going to be tough for me to play here," he added. "But once you get out on court, you try your best. It was just too tough for me to play with two problems."
World number 79 Kuznetsov sealed the victory with his sixth ace of the match and will meet South African Kevin Anderson or Paolo Lorenzi of Italy in the second round.
Monaco reached a career high world number 10 last season after winning four tournaments and said he was confident he would be fit to play again in the next couple of weeks.
"I have to look forward," he said. "The South American swing is coming soon and that's on clay, which I love.
"In 10 to 15 days, I'm going to be ready for sure."
Djokovic, looking to rewrite the Australian Open record books, opened with a 6-2 6-4 7-5 victory over France's Paul-Henri Mathieu.
The 25-year-old Serb is attempting to win his third successive Australian Open title, and fourth overall. No man in the professional era has won three successive Australian titles.
The match could have been a potentially tricky one for Djokovic.
Mathieu was a former top-20 player, rising to as high as 12th in 2008, before he underwent knee surgery in 2011 that wiped out his entire season and dropped him down the rankings.
"I was very committed from the start of this match... because I knew the quality of my opponent," Djokovic said. "He has been on the tour for a while and he played the finals of Davis Cup.
"He had lots of success (and) he can go out there and play equally well as anybody if it's in his striking zone."
The 31-year-old Frenchman did show glimpses of the prowess that carried him up the rankings, with tactical awareness and an ability to construct, then finish points, though Djokovic said he felt comfortable throughout.
"You know, I felt I was in control of the match in the opening two sets," Djokovic said.
"Then, you know, he started playing better, striking the ball quite well from both sides on the baseline.
"I thought he was serving really precisely and really well. It was tough to break."
Despite Mathieu's improved performance, Djokovic showed why he was world number one late in the third set.
Twice Mathieu had him scrambling, wrong footed and off balance. And twice, a lunging Djokovic was able to recover with heavy topspin forehands to pass the Frenchman at the net.
The first curved acutely across court to clinch the 10th game of the set for the Serb, while the second went like a bullet down the tramline to set up a break in the 11th that eventually gave him the chance to serve for the match.
He achieved victory with a forehand pass before celebrating with his customary fist pump salute to his supporters.
The world number one will now meet Ryan Harrison of the US in the second round after the American had earlier overcome Colombia's Santiago Giraldo 2-6 6-4 7-5 6-4.
"He's one of these up-and-coming young talents who has been playing well on the tour for last few years," Djokovic said of the 20-year-old American.
"He likes playing on hard courts. I think he had lots of success in U.S. hard court tournaments. He has a big serve which he likes to use and big forehand.
"I played him few times before on different surfaces. I know what it takes to win that match."
Fourth seed David Ferrer eased through in three sets against Olivier Rochus.
The Spaniard's 6-3 6-4 6-2 victory on Hisense Arena arrived courtesy of 29 unforced errors from the Belgian.
Ferrer won the Auckland warm-up tournament last week but is not thinking about how far he can go in Melbourne with compatriot Rafael Nadal absent through illness and injury.
"The top four players are better than there ever was," Ferrer said. "In the last years they were in the semi-finals and finals all the time. It's very difficult for a top player to win their first Grand Slam, but I am trying to do my best every match.
"I never think if I can do semi-final or quarter-final, I am only focused on my next opponent."
Fifth-seed Tomas Berdych made light work of Michael Russell, beating the American with a 6-3 7-5 6-3 victory to move into the second-round.
Berdych, a Grand Slam finalist at Wimbledon in 2010, could only manage to convert half of his first serves but with Russell - the oldest man in the draw - making 42 unforced errors, the Czech's work was made easier.
Berdych said afterwards that a run deep into the tournament would mean a lot to him given the incredible standard at the top of the men's game.
"If you look at the draw, if you want to win a Slam and you have to beat at least three of them, then it's really tough," he said.
"That's how it is. Today's tennis is really, really strong. I think we are in the best era of our sport ever. It's the same for everybody. I think we are all trying our best to break that huge barrier in front of us.
"If this happened for me, then it would be I would say at least 10 times better than it would have been before."
Janko Tipsarevic emerged triumphant from an entertaining 7-6(4) 7-5 6-3 battle with former world number one and home hope Lleyton Hewitt which lasted three hours.
The eighth seed managed 47 winners but made 38 unforced errors while Hewitt, playing in a record 17th consecutive Australian Open, sent down 40 winners but committed 48 mistakes of his own to bow out.
"I gave 100 percent," Hewitt said, having shown flashes of his former brilliance and his usual fist-pumping swagger. "I was pretty happy with my ball-striking, just frustrated with the result."
The Serb will play Slovakia's Lukas Lacko in the second round.
Nicolas Almagro opened his campaign with a tough five-setter, the Spaniard eventually prevailing 7-5 6-7(4) 6-2 6-7(6) 6-2 against another American Steve Johnson.
In a match lasting over three hours, the qualifier from the States pushed the 10th seed all the way, although Almagro's experience ultimately told.
France's Julien Benneteau, raised into the 32nd and final seeding position after the withdrawal of John Isner, was the first man to taste victory in Melbourne this year when he thrashed rising Bulgarian talent Grigor Dimitrov 6-4 6-2 6-4.
Dimitrov, 21, has been nicknamed 'Baby Fed' because of his precocious talent but has yet to get past the second round at a Grand Slam in 10 attempts.