Williams, five times a singles champion in Melbourne, won their only previous encounter 6-1 6-2 back in 2008, but here she was even more dominant, winning 6-0 6-0 against an opponent who simply had no answers to her power and precision.
The only bump in the road for the third seed was a heavy fall on the Hisense Arena court midway through the first set which led to a lengthy break in play as she had her ankle treated, but even that could not help Gallovits-Hall, ranked 110th in the world, get on the board.
Next up for Williams - assuming there is no lasting damage to her ankle - will be either Slovakia's Magdalena Rybarikova or Garbine Muguruza of Spain.
Top seed Victoria Azarenka survived a second-set scare to see off Monica Niculescu.
Having cruised through the opener Azarenka's game inexplicably came off the rails in the second before she reasserted her superiority to win 6-1 6-4.
Cheered on by close friend Redfoo from the band LMFAO, it was her first appearance at the Rod Laver Arena since her thrashing of Maria Sharapova in last year's final.
Azarenka admitted afterwards she was pleased to have avoided an embarrassing return to Melbourne
"It's great to be back, there were a lot of overwhelming emotions out there," she said.
"I started really well but the second set was a struggle. I am pleased to get through."
Laura Robson, the British number two, advanced past the first round of the Australian Open for the first time in her career with a hugely impressive straight-sets victory over Melanie Oudin.
The 18-year-old, born in Melbourne, dominated from the outset with her crushing groundstrokes to go through 6-2 6-3 in 75 minutes to set up a match with Petra Kvitova.
Japan's Kimiko Date-Krumm produced the biggest shock of the Australian Open so far when she unseated 12th seed Nadia Petrova 6-2 6-0 to become the oldest winner of a women's singles match at the tournament.
The 42-year-old, playing in her 11th Australian Open 23 years after her debut, was well worth the quick-fire victory, which she sealed on her second match point when her Russian opponent hit a forehand wide.
Date-Krumm reached the semi-finals at Melbourne Park in 1994, where she lost to Steffi Graff, but had not won a match at the year's first grand slam since returning after a gap of 12 years in 2009.
The world number 100 will face Shahar Peer of Israel or another Russian in Alexandra Panova in the second round.
Former world number one Caroline Wozniacki was pushed hard by Germany's Sabine Lisicki before rallying in the third set to move into the second round.
The Dane, who finished 2010 and 2011 as the world's top-ranked player, has been struggling this year and was bundled out of the Brisbane International in the first round before falling at the second hurdle in Sydney.
Now ranked 10, her lacklustre form appeared to be continuing on the Hisense Arena at Melbourne Park before she reeled off six third set games in a row to go through 2-6, 6-3, 6-3.
Roger Federer opened up his Australian Open challenge - and his season - with a routine straight-sets victory over France's Benoit Paire.
The second seed came to Melbourne having played no warm-up tournaments, but showed no signs of rustiness as he kicked off his bid for a fourth Australian Open title with a 6-2 6-3 6-1 win over the world number 46 in just 83 minutes.
For Paire, who deals more in spurts of inspiration than the sustained brilliance of Federer, it was a painful experience and by the end he looked keen to get off court as quickly as possible.
Federer said: "Benoit's a good player, a good talent. I haven't played a match this season yet. You're not sure [how you're going to play] and that's why you're relieved when you get through the first one."
Jo-Wilfried Tsonga beat Michael Llodra in 6-4, 7-5, 6-2 at the Hisense Arena to get his tournament under way, while sixth seed Juan Martin Del Potro defeated French qualifier Adrian Mannarino 6-1, 6-2, 6-2 in his opening match.
Andy Murray looked every inch a grand slam champion with a near-flawless display to brush aside the challenge of Robin Haase at the Australian Open today.
The world number three claimed beforehand he was stepping into the unknown as he set out to win one of the game's four biggest prizes as a major winner for the first time following his success at the US Open in September.
But the early impressions were that he was quite comfortable with his newly-elevated status as he proved too good for dangerous Dutchman Haase, winning 6-3 6-1 6-3 in one hour and 37 minutes.
"It was a good start and nice to win in straight sets," said Murray.
"It was the hottest day we have had for a while and the court was playing quicker so it's nice to get through."
Next up for Murray is Joao Sousa, who beat Australian wild card John-Patrick Smith in straight sets.