The Brazilian comfortably beat the world number six 6-3 6-2 to claim his first victory over his opponent in four attempts.
"I didn't play very well, but my opponent, he was better than me in the first and second set, in every moment," said last year's runner-up.
"I made lots of mistakes. I am not fast. He plays very aggressive, very consistent. He was better."
Bellucci will now take on the Netherlands' Robin Haase in the next round.