Miami has been a successful destination for Norrie in recent years, with the 27-year-old winning the biggest title of his career there in 2021 and reaching the quarter-finals in last year’s edition.
However, Norrie was simply outclassed by Barrere on Saturday, with the world number 65 wrapping up a 6-3 6-2 victory in an hour and 10 minutes.
After trading holds early, Barrere was able to strike first blood by breaking Norrie’s serve in the eighth game.
Norrie could only mount mild resistance from there, as Barrere cruised home in the second set to book a third-round meeting with Christopher Eubanks.
The American qualifier recorded the biggest win of his career so far as the world number 119 knocked out 17th seeded Croatian Borna Coric 3-6 6-4 6-2.
Meanwhile, British number two Dan Evans saw his losing streak extend to six matches after Italian Lorenzo Sonego came from behind to win 4-6 6-3 6-2 in two-and-a-half hours.
Evans had started brightly, securing an early break in the first game and then held to lead 2-0 before closing out the first set.
However, Sonego, the world number 59, rallied to break Evans in the fourth game of the second set before maintaining a vital hold in the next game which allowed him to level the match.
The momentum remained with the Italian, who broke twice in the deciding set as he opened up a 4-0 lead and never looked like allowing Evans back into the match.
Elsewhere, Jiri Lehecka continued his impressive form to reach the third round of an ATP Masters 1000 event for the first time.
The 21-year-old Czech, a quarter-finalist at the Australian Open, beat 18th seed Lorenzo Musetti 6-4 6-4.
Second seed Stefanos Tsitsipas was handed a walkover into round three after Frenchman Richard Gasquet was forced to withdraw because of an ankle injury.
Fourth seed Daniil Medvedev barely broke a sweat against Roberto Carballes Baena of Spain, winning 6-1 6-2 in just over an hour.
Fifth seed Felix Auger-Aliassime of Canada beat Brazilian Thiago Monteiro 7-6 (5) 7-6 (8) and will next play Francisco Cerundolo, who was a 6-4 6-4 winner over American lucky loser Aleksandar Kovacevic.
Eight seed Hubert Hurkacz of Poland outlasted Australian lucky loser Thanasi Kokkinakis 6-7 (10) 7-6 (7) 7-6 (7) in a gruelling three-and-a-half hour affair.
Karen Khachanov, the 14th seed, held off a brave effort from Tomas Martin Etcheverry to claim a 6-1 3-6 6-3 victory.
Number 15 seed Alex de Minaur suffered an unexpected defeat to French debutant Quentin Halys, who progressed through a marathon three-hour, 18-minute match 6-7 (5) 7-6 (3) 7-6 (8).
Chilean qualifier Cristian Garin also advanced to the third round with a 7-6 (2) 6-3 win over Argentina’s Sebastian Baez and will go on to face Tsitsipas.
Adrian Mannarino defeated Ben Shelton in three sets, while 12th seed Frances Tiafoe came back from a set down to beat Japanese qualifier Yosuke Watanuki 6-7 (5) 7-6 (3) 6-4.