The straight-sets victory saw the British number three, ranked 102nd in the world, ease past his 266th-ranked opponent.
21-year-old Norrie was much more assured in the second set as he was able to get more consistency from his serve.
Kenin and Garcia deserve respect for finding strength to split from father-coaches
His opponent in the second round will be the Germany Maximilian Marterer, who defeated Gael Monfils 2-6 6-4 6-4 in his first round tie.
There was good news in the qualifying of the French Open, as 19-year-old Briton Jay Clarke beat India's Ramkumar Ramanathan 6-3 5-7 6-1 to set up a tie with the Australian Bernard Tomic in the third round,
Norrie misses out on Djokovic duel with defeat at Italian Open
In-form Norrie battles past Carballes Baena in straight sets