The defending champion is still yet to drop a set while sailing through to the last 16, where he will take on Jannik Sinner in a repeat of last year's quarter-final clash between the pair.
Nadal was not at his absolute peak against Norrie – he committed 29 unforced errors and had problems holding his serve in the second set, though the Spaniard still produced when it mattered to beat the Briton comfortably enough.
A solitary break was enough to take the opening set, but the No.3 seed was made to work hard in the next – at one stage even finding himself 3-1 down.
After a backhand winner put him up 40-30 in the fourth game, Norrie flashed a fabulous forehand past his opponent to register a second successive break. Crucially, though, he could not consolidate on each occasion.
Indeed, Nadal claimed the next five games as he seized control in imperious fashion, wrapping up the second set after 42 minutes courtesy of a stunning passing shot that was followed by a roar of approval towards his watching team.
With his forehand now in full flow, Nadal motored towards the finishing line in the third and final set.
A break in the fourth game edged him in front and while unable to seal the result at the first attempt when having a match point on his opponent's serve, the king of clay fashioned yet another straight-sets win in the French capital.
Norrie made him work to the very end, at one point sitting at 30-30 in the ninth game, but the relentless pursuit of a record-extending 14th French title continues for Nadal.
Nadal is now 103-2 for his career at the French Open and is unbeaten in his previous 33 outings at the event. Such is his dominance, the left hander has secured 32 sets in a row since he lost the second in the 2019 final against Dominic Thiem.