Norrie was ranking world number 41 at last year’s French Open – his highest career ranking
British number two Cameron Norrie beat Taylor Fritz of the United States 6-4 6-7 6-4 at the Delray Beach Open in Florida on Tuesday.
The 24-year-old, who is ranked world number 60, will play Brandon Nakashima in the second round on Wednesday.
British number three Kyle Edmund, who won the New York Open title on Sunday, withdrew from his first round match against Ugo Humbert because of illness.
Top seed Australian Nick Kyrigos withdrew with a wrist injury.