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.
The match could hardly have got off to a worse start for the Romanian as she double-faulted to give Williams a break in the first game.
And there was more of the same as the American overwhelmed her opponent with her powerful groundstrokes to make it 3-0.
At 4-0, Williams suffered a scare as she slipped on her heavily-strapped right ankle while chasing down a forehand and crashed to the ground.
She eventually limped back to her seat and the trainer removed the bandaging from her foot to administer treatment.
After having the strapping re-applied, Williams was okay to continue and she showed there was no lasting damage by hammering three colossal forehand winners in the next four points points on her way to a third break and a 5-0 lead.
Williams received more treatment at the change of ends but held to 15 to seal the first set.
The second set started just as the first had - with Gallovits-Hall double-faulting to give Williams an opening break.
She broke to love in game three and had help from yet another Gallovits-Hall double fault - her eighth - to make it 5-0, before serving out another love game to complete the most comprehensive of victories in 54 minutes.
Gallovits-Hall produced just one winner to Williams' 18, and only won only 18 points in total.
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.