"This was one of the toughest matches I have ever played. I am glad I am through," Massu said.
He was joined in the final four by Argentines Gaston Gaudio and Mariano Zabaleta.
The third-seeded Gaudio eliminated No. 6 Mikhail Youzhny of Russia 6-4, 4-6, 6-4, while Zabaleta beat fifth-seeded Spaniard Feliciano Lopez 6-4, 6-2.
Massu will next face unseeded Spaniard Fernando Verdasco, who beat the Romania's Victor Hanescu of 6-3, 6-3 to reach the final four for the second straight year. Massu was broken on his opening service game, double-faulting twice and committing two unforced errors.
"That was bad, it woke me up," said Massu, who recovered by breaking Lapentti twice to lead 5-2. Lapentti, the 2001 Generali Open champion from Ecuador, saved three set points and pulled within 4-5 before finally succumbing.
Second-seeded Guillermo Coria ousted French Open champion Juan Carlos Ferrero 6-3, 6-0 to advance to the semifinals of the Croatia Open.
A finalist at two ATP Masters Series events this year, Coria broke at 3-3 and 5-3, winning the final 10 games to claim the match.
It was Coria's first tournament since Wimbledon, and the Argentine clay-court specialist said he felt like he could go all the way to win his first title of the year.
"I feel good and I think I'm on the right track," he said.
Coria faces Italian Filippo Volandri in the semifinals. Volandri, a finalist at the Croatia Open the last two years, rallied to upset third-seeded Tommy Robredo of Spain 3-6, 6-3, 6-3.
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