He said: “I served much better than last week, and I was a bit more patient and knew I had to play point for point and really make the rallies a bit longer.
“I think I learned from last week with that, and just happy to be back in Brazil.”
Norrie will face Chilean Tomas Barrios Vera next, after the world number 120 beat Brazilian wild card Gustavo Heide 7-5 6-3.
Norrie won the top prize at last year’s Rio Open, defeating world number two Carlos Alcaraz in the final. There was more British success in Mexico as Dan Evans beat fifth seed Roman Safiullin 6-2 6-4.
Evans was denied an all-British meeting in the last 16, however, as Jack Draper was beaten in three sets by Australian Thanasis Kokkinakis. Draper took the first set but the Australian hit back to win 4-6 7-6 (5) 6-4.
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