Paire is not short on talent, with his backhand one of the best around, but his effort has often been called into question and he barely seemed to try during the first and third sets in sweltering conditions.
Norrie lost just 17 points in the two sets combined either side of a highly competitive second and wrapped up a 6-0 7-6 (1) 6-0 victory in an hour and 40 minutes.
The British number one is playing as a top eight seed at a grand slam for the first time and is firmly in the conversation as a contender for the title, particularly after his run to the Wimbledon semi-finals.
It would be hard to find two tennis players with more different attitudes to their sport and Norrie was focused from the start while Paire made 16 unforced errors - twice the number of points he won - and hit only one winner in a first set that lasted less than 20 minutes.
The second was a different story and, after a brief delay when a spectator collapsed in the stands, Paire broke the Norrie serve to leave himself serving for the set at 5-3.
However, Norrie broke back straight away, dominated the tie-break and, with Paire barely jogging around the court in the third, quickly completed the job.
He’s joined in the second round by Daniel Evans, who became the third British male singles player through to the next round in New York.
The 20th seed beat Jiri Vesely 6-4 6-1 6-1 in routine fashion, in what was Evans’ first match since losing in the opening round in Cincinnatti a couple of weeks ago. He faces either James Duckworth or Chris O’Connell next.
“It’s been quite a while since Cincinnati but it was nice to get out and I played very well,” Evans said.
“I played well the week before and I didn’t play great in Cincinnati but it’s the first round and the start of a new tournament and you have to start building again.
“I didn’t do too much running, I served well and dictated pretty well.”