It was an encouraging display for the Spaniard's fans ahead of the Paris Olympics.
The 38-year-old, who opted to miss Wimbledon in order to focus efforts on the Games, had his serve broken by fifth-seed Norrie, who was looking to level the match after going down 6-4 in the first set.
But having received treatment on court to his arm after talking a heavy fall, Nadal came back to claim a 6-4 win in the set and progress to the quarter-final where he will face Argentinian Mariono Navone.
"Great feelings, it's been a while without playing on the Tour since Roland Garros and I had a chance to compete against a great player like Cameron," said Nadal.
"It's part of the journey today. I haven't been competing very often so matches like today help and holding the pressure on the opponent for the whole game is something I need to improve on because I haven't played enough."
Nadal, who will play singles and doubles with Carlos Alcaraz in Paris, where he became a record 14-times French Open winner, broke Norrie once in the first set to set up what at the stage looked like being a routine win.
But having fallen behind in the second set, he required a five-game winning run in order to edge through.
He will play the doubles semi-final with Casper Ruud on Saturday.