The British No1, seeded No11, 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, who next faces another French player in Constant Lestienne, said: “It took a little bit to find my range with the ball but for me it was a solid day.
“I served for the first set twice and didn't play the best game, but played a good tie-break, and then I won nine games in a row and was looking good to keep going and ended up winning in straight. I'll take that after a quick turnaround.”
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.
Elsewhere, Jack Draper lost his first-round tie with Nadal as Emma Raducanu shrugged off injury concerns to win comfortably.
Harriet Dart was unable to capitalise on a good start against 32nd seed Jil Teichmann.
The British No2, playing in the main draw on ranking for the first time here, led the Swiss player 4-2 and should have broken again to lead 5-2. But Teichmann fought back and was too solid for Dart in the second set of a 7-5 6-1 victory.
Additional reporting by PA.