The second-seeded Ferrero beat fellow Spaniard Alex Corretja, 6-4, 6-4. Their countryman, the third-seeded Moya, defeated Max Mirnyi of Belarus, 6-4, 6-4, and No. 4 Federer topped Argentine Mariano Zabaleta, 7-6 (7-4), 6-2.
Verkerk eliminated Roddick, 6-7 (6-8), 6-3, 6-4, to reach the third round of the $2.33 million claycourt Tennis Masters Series event.
The 23-year-old Ferrero is off to a career-best 30-6 start this season and won for the 19th time in 20 claycourt matches. He won his first title of the year last month at the Monte Carlo Masters and claimed the Valencia Open on Sunday.
Ferrero raised his record in Rome to 11-2, having won the crown two years ago. He will face No. 15 Guillermo Coria of Argentina in the next round. Coria defeated Romanian qualifier Victor Hanescu, 6-1, 7-6 (8-6).
Federer is also coming off a title, having earned his third tournament triumph of the year Sunday in Munich. The Swiss star won his tour-best 34th match Wednesday.
Spain's Tommy Robredo will be Federer's third-round foe after crushing Juan Ignacio Chela of Argentina, 6-0, 6-2. Robredo, who reached the quarterfinals here last year, lost his two previous meetings with Federer.
Moya won for the 21st time in 23 matches on clay this season and recorded his 30th match victory overall. Coming off a title run in Barcelona two weeks ago, he will be looking to reach the quarterfinals for the first time in eight trips to Rome. The 26-year-old Spaniard will have to get past Yevgeny Kafelnikov in the third round.
Kafelnikov continued his best clay campaign since winning the French Open in 1996 with a 7-5, 6-1 victory over Italian wild card Giorgio Galimberti. Making his 10th appearance in Rome, the 29-year-old Russian has never gone beyond the third round.
Verkerk, 24, raised his season match record to just 10-12. He captured his first ATP title in Milan in February.
Roddick endured his fourth early-round loss in nine tournaments this season. Twice a finalist his year, he reached the semifinals in his Rome debut last season.
Roland Garros' reigning champion, seventh seed Albert Costa of Spain, rallied past Arnaud Clement of France, 6-7 (3-7), 6-2, 6-4. Costa, the 1998 runner-up, has had advanced past the third round just once in eight tournaments.
Also, eighth seed Jiri Novak of the Czech Republic eased past Dominik Hrbaty of Slovakia, 6-1, 6-4, and No. 12 Rainer Schuettler of Germany beat South African Wayne Ferreira, 7-6 (8-6), 6-2, despite suffering from a fever.