The British number one, seeded 11, has become a master of winning these early grand-slam matches and so it proved once again, a run of 10 straight games helping him to a 7-6 (3) 6-0 6-3 victory over a player ranked 143.
Norrie only arrived in Melbourne late on Saturday night after a heart-breaking loss to Richard Gasquet in the final of the ASB Classic in his home city of Auckland.
That gave him only one day to prepare for this match but he carried a lot of confidence from a run of six victories to start the season, including over Rafael Nadal, as well as his exploits of the last two campaigns.
A good run here could see Norrie return to the top 10 and he was his customary relentless self as he wore down 18-year-old Van Assche.
The Frenchman, who won the junior title at Roland Garros in 2021, is considered a big talent for the future and twice recovered from a break down in the opening set.
Norrie became a little wayward off his forehand but tightened things up in the tie-break and from there kept constant pressure on Van Assche, who will have learned a lot from the encounter but was not quite up to the task here.