There was little to separate the pair throughout the match, but Ferreira was more aggressive and better at taking any opportunities that fell his way.
The 11th-seeded Brazilian had the early advantage, breaking for 2-1 and holding two break points in the fifth game after Ferreira had levelled at 2-2.
Kuerten also led 4-1 in the tiebreak before surrendering the next six points, and the former French Open champion was broken at 4-4 in the second set to leave Ferreira serving for victory.
"There really wasn't much in it," said Ferreira. "In the first set I struggled with my serve and didn't get any free games. It was a close set, and winning it was a big edge.
"I think if I had lost that it might have been a littlebit difficult. The second set was more in my favour. I served a lot better and got through my service games a lot easier, and still made him work hard on his."
Unseeded Olivier Rochus of Belgium followed up his second round win over reigning French Open champion Albert Costa by ending the run of Britain's Tim Henman.
Although Henman played well on occasions, Rochus won the first eight points of the first set and the last 12 before taking a 4-0 lead in the second on the way to a 6-4, 6-3 victory.
"There were some good periods, but it's something you have to string together a bit longer," Henman said. "You look at the overall consistency of his performance, and it was certainly a lot better than mine, and when he had to produce something extra he hit some great passing shots and drop shots.
"But it has been a positive week for me, and something I can build on for Roland Garros."