Serving for the set, Murray was 40-0 down before getting to deuce with a backhand that just caught the line.
He then secured victory in two hours 16 minutes when Etcheverry, ranked 30th in the world, sent a forehand long and wide on match point.
Overall, Murray served 10 aces, hit 28 winners compared to 17 from his opponent, and saved seven of seven break points.
He will play Tomas Machac, who is 60th in the men’s rankings, of the Czech Republic in the last 32.
Murray is a two-time champion of the tournament but this is expected to be his final appearance in Miami as he plans to retire later this year.
“Miami has been like my tennis home really. I’ve done so much of my work and training and preparation here, and I love the city – and this is my last time playing here, so it’s nice to get another opportunity,” he said.
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