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.
Dan Evans swept aside Jiri Vesely to become the fifth British player through to the second round.
With defending champion Emma Raducanu still to play, this is already the joint most British players to reach the second round in New York since 1981, with Evans joining Andy Murray, Norrie, Jack Draper and Harriet Dart.
Evans reached the fourth round here last year and arrived at Flushing Meadows buoyed by a run to the semi-finals of the ATP Tour event in Montreal earlier this month.
And he was ruthless against Czech Vesely, wrapping up a 6-4 6-1 6-1 victory in and hour and 55 minutes in brutally hot conditions.