Costa, the 2002 winner at Roland Garros, defeated 12th-seeded Jiri Novak of the Czech Republic 6-4, 6-2, showing his clay-court game is rounding into shape.
The Italian Open is a big tuneup for the French Open, which starts on May 24 and is the only major played on clay.
"When he's motivated and playing well with confidence, he's a top-five player on clay," Moya said of Costa. "We know each other since we're 16, 17. Him winning at Roland Garros shows how good he can be when he's playing well."
Moya and Costa will meet a pair of Argentines, David Nalbandian and Mariano Zabaleta, in Saturday's semifinals. The draw, which reads like a Davis Cup tie between Spain and Argentina, is Moya against Zabaleta, and Costa facing Nalbandian.
On Friday, Zabaleta broke serve to go up 6-5 and served out his 6-1, 7-5 win against Chile's Nicolas Massu. Nalbandian won six straight games after falling behind 3-0 in the second set and finished with a 6-4, 6-3 victory against American Vince Spadea.
"We know how the Argentines can play, not only on clay, but everywhere," Moya said. "Hopefully, we will have an all-Spanish final."
Costa dismissed Novak in little more than an hour, never losing serve and snapping forehands at will from beyond the baseline.
Ranked just 65th, Costa is almost always a threat on clay. In addition to his success in Paris, including a semifinal appearance last year, Costa has reached the semifinals in Rome three times. In 1998, he had to pull out of the Foro Italico final with a wrist injury, and in 1996 he lost to eventual champion Thomas Muster in the semifinals.
On Wednesday, Costa upset top-ranked Roger Federer in three sets.
His results in Rome are a sharp turnaround from his straight-set, first-round loss to Albert Montanes in Barcelona last week. After that match, Costa said he was lacking motivation.
"I talked with a lot of people, also with a therapist, just to try to find a way out," Costa said. "She counseled me to find motivation inside myself. I go from time to time when I feel I'm not comfortable."
Moya, who defeated qualifier Ivo Karlovic of Croatia 6-4, 3-6, 6-4 in a rain-delayed third-round match earlier Friday, said his first match of the day helped him ease past Pavel.
"I had trouble to beat Karlovic, but I think that gave me a lot of confidence to go on the court tonight and play well," he said.
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