Sixth seed Söderling, who reached the French Open final for the second time earlier this month, won 6-4, 6-2, 7-5 in an hour and 54 minutes on Court One.
Söderling had two match points on the 25th seed’s serve and won it when the Brazilian number one fired long.
The Swede faces Spanish ninth seed David Ferrer in the round of 16.
“It’s been really good so far, I think I’m serving well and I’m hitting the ball really well,” Söderling said.
“I was a little bit lucky to get away with this one in straight sets.
“I’m definitely having more confidence. I’ve played really well the last year and a half.
“Confidence is a big thing and I think what helped me most is that I’m playing well in the really important moments.”
Söderling said he was often in touch with Björn Borg but had not heard from the Swedish tennis legend so far in the championships.