Haase represented a potentially tricky first assignment for the world No 3 but the Dutchman was never allowed to get into his stride as Murray dominated in a 6-3 6-1 6-3 victory.
It was as good a first-round performance as Murray has delivered in recent years and he was pleased with how he coped in the oppressive heat on Rod Laver Arena.
“It was a good start,” he said. “It was very different conditions to what it’s been like the last four, five days. The court was playing different, much livelier.
“But I thought I did a pretty good job from the start – dictating the points and not giving him too many freebies.”
It was Murray’s first grand slam match since he claimed his maiden major at the US Open last year but he said he was still nervous beforehand.
“I don’t think there is anyone who doesn’t get nervous,” he said. “Nerves are a good thing. If you aren’t nervous, it shows that you’re really not that bothered.
“I started the year well in Brisbane but coming into the slams the first match is normally pretty tough.
“You just have to focus and play solid, not make too many silly mistakes. I did a good job of that today.
“It is always nice to get through the first round of any tournament but especially here.”
Murray trailed the world No 53 by two sets before coming through their second-round encounter at the 2011 US Open and the memory of that scare may have been behind the Scotsman’s fast start.
He broke for a 2-1 lead at the second opportunity – after narrowly missing on the first with an improvised flick up the line.
Although Haase was holding his own in the majority of the hard-hitting early exchanges, Murray found a way to break through once again for 4-1 when his opponent went long on a routine backhand.
A wobble saw Murray have to save five break points as Haase started to go for broke, especially on the third seed’s slightly suspect second serve, and the Dutchman did break through two games later to reduce the deficit to 5-3.
But Murray simply raised his level to take the Haase serve immediately and win the first set in 41 minutes.
Murray broke for a 3-1 lead and then again for 5-1 after his opponent dumped a dispirited forehand into the net.
The standard had dropped from early on but Murray was still making remarkably few unforced errors, especially compared with Haase, who was starting to display his erratic side. Murray served it out to take it 6-1 and establish a two-set advantage.
The third was a procession as Murray cruised into a 4-1 lead without breaking sweat.
Haase got one of the breaks back but it did not prove particularly damaging as Murray simply hit back to complete a hugely-impressive opening-round triumph.
Next up is a match with world No 100 Joao Sousa after the Portuguese beat Australian wild card John-Patrick Smith in straight sets.
Roger Federer came through his first competitive match of 2013 by thrashing Benoit Paire.
Federer opted to skip the usual warm-up tournaments and instead played a series of exhibition events in South America but hit the ground running in Melbourne with a 6-2 6-4 6-1 victory in which he was rarely troubled.
Federer said: “Benoit’s a good player, a good talent. I haven’t played a match this season yet and you’re not sure how you’re going to play. That’s why you’re relieved when you get through the first one.”
Jo-Wilfried Tsonga, the runner-up here in 2008, is regarded as a threat to the “big three”, and he looked good in seeing off Michael Llodra 6-4 7-5 6-2.
The same applies to Argentinian Juan Martin Del Potro, who dropped just five games in beating qualifier Adrian Mannarino.
Canadian Milos Raonic lost the first set but hit back to beat Jan Hajek in four while there were also wins for ninth seed Richard Gasquet, 12th seed Marin Cilic, 17th seed Philipp Kohlschreiber and 21st seed Andreas Seppi.
In the late match, Bernard Tomic, the talented young Australian who claimed his first title in Sydney last week, proved far too strong for Leonardo Mayer, winning 6-3 6-2 6-3.
Serena Williams suffered an injury scare but insisted she would be fit for her second-round encounter tomorrow “unless something fatal happens”.
Williams suffered a heavy fall during her crushing 6-0 6-0 win over Edina Gallovits-Hall, damaging her right ankle and having to undergo lengthy treatment.
But the American, chasing a fifth title in Melbourne, was adamant she would return to court to face Garbine Muguruza.
Top seed Victoria Azarenka also suffered a scare before beating Monica Niculescu 6-1 6-4.
Azarenka, the defending champion, ran through the first set only for Niculescu to swiftly establish a 3-0 second-set advantage. It almost became 4-0 but Azarenka staved off two break points. It proved a turning point as the world No 1 hit back.
Former world No 1 Caroline Wozniacki produced a wonderful deciding set comeback against Sabine Lisicki, who led 3-0 in the third only to run out of steam as 10th seed Wozniacki hit back to win 2-6 6-3 6-3.
Eighth seed Petra Kvitova eased past Francesca Schiavone in three sets in a battle of former grand slam champions.