Ferrero, the top seed from Spain, was joined as a third-round winner by second seed Carlos Moya, who let a 5-3 lead in the second set slip against Dominik Hrbaty and had to struggle before salvaging a 6-1, 6-7 (5-7), 6-3 triumph.
But two other members of Spain's powerful Davis Cup team went down defeat on the home clay of the Real Club de Tenis. Defending French Open champion Albert Costa and two-time Roland Garros finalist Alex Corretja both lost.
Argentine 16th seed Agustin Calleri, a finalist this month at Estoril, upset the third-seed Costa, 6-4, 6-2, the Spaniard's second major loss in as many weeks.
Costa was beaten in the first round at Monte Carlo by 16-year-old compatriot Rafael Nadal and has to be doubting his preparation plans for next month's defense of his Grand Slam crown.
"I just haven't been able to readjust to playing on clay," said the 27-year-old Costa, who reached the hardcourt Miami semifinals in march. "He played well but really I made it easy for him."
Spanish 12th seed Tommy Robredo knocked off the 29-year-old Corretja in a 7-6 (7-4), 6-7 (1-7), 6-2 struggle which left the veteran slamming his racket in frustration.
Kuerten set up his quarterfinal clash with Ferrero without playing a shot as ninth-seeded Moroccan Younes El Aynaoui pulled out prior to their match with a fever.
The unexpected exit took Kuerten by surprise.
"I won't take this for granted," said the three-time Roland Garros winner. "But I want to forget that I got a walkover."
Ferrero led Volandri 5-1 in their opening set, but the challenger started to threaten, saving three set points in the eighth game and breaking for 3-5 before the top seed claimed the set with an ace.
In the second set, Ferrero broke at for 5-4, then served out the victory a game later.
"It will be a tough test against (Kuerten), but a good match for the fans," said the winner, who is aiming for a second title in a row after Monte Carlos last weekend. "I'll be giving my all here for the Barcelona crowd."
Fourth seed Marat Safin, the 2000 champion, kept up the improvements to his clay game in his first tournament of the year on the slow, steady surface.
The Russian, a former U.S. Open winner, defeated Finland's Jarkko Nieminen, 6-3, 6-3.
"I need hard matches to build up my confidence again," said Safin, "I want to win tournaments and find the points again."
Gaston Gaudio, the 10th seed from Argentina, defeated David Sanchez of Spain, 7-5, 4-6, 6-2 and Russian Nikolay Davydenko, the Estoril champion, defeated Jose Acasuso of Argentina, 6-4, 6-3.