French Open champion Gaston Gaudio slumped to a 6-0, 6-1 defeat by Spain's David Ferrer, and fourth seed Tim Henman lost 6-3, 3-6, 6-3 to Dominik Hrbaty of Slovakia.
The exodus of leading players left Spanish teenager Rafael Nadal as the highest-ranked player in the draw. The fifth seed, who has won four claycourt titles this year, continued his run of superb form with a 6-3, 6-1 victory over Guillermo Canas.
One set down and serving at 3-5 and 0-40 in the second, Verdasco seemed on the brink of defeat against Roddick -- even more so when his second serve was called out and the umpire started to announce the American as the winner.
Roddick, however, corrected the call, telling the umpire the ball was in. Verdasco went on to hold serve and break his distracted-looking opponent in the following game.
The set went to a tiebreak, which the Spaniard took easily with a series of whipped crosscourt winners.
Roddick then put a forehand wide to drop serve in the opening game of the decider and the unseeded Verdasco went on to claim victory.
His reward will be a quarter-final against fellow claycourt specialist and number nine seed Guillermo Coria of Argentina, who crushed home favourite Davide Sanguinetti 6-0, 6-4.
"Maybe I should have stood on the mark," Roddick told reporters. "I don't think I did anything extraordinary, the umpire would have come down and said the same too.
"I just saved him the trip.
"When he (Verdasco) hit it, before I saw the mark, I thought it was out. On a hardcourt I wouldn't have done anything but then I walked back and saw it was good."
Roddick was generous in praise of Verdasco and spoke of his own improvement on a surface that does not favour his serve-and-volley style.
Before losing in the Italian capital he had won seven matches in a row on clay, including his run to the U.S. Claycourt title in Houston last month.
180 DEGREES
"Sometimes you feel you've done something wrong and deserve to lose the match. That wasn't the case today. He just went for broke," Roddick said.
"In the (second set) tiebreak I didn't play a single bad shot...he was playing with confidence, he just turned 180 degrees.
"Compared to where I was (on clay) last year, though, I'm improving. I was a point away from the quarters here and I'll continue my preparation for (the French Open at) Roland Garros (at the ATP tournament in Hamburg) next week."
Briton Henman also tumbled out when he lost 6-3, 3-6, 6-3 to Slovakia's Dominik Hrbaty but sixth seed Andre Agassi remained on course to repeat his 2002 victory in Rome.
The 35-year-old American gave a near-faultless display to defeat Ivan Ljubicic 7-6, 6-3.
The big-serving Croatian has reached four finals this year and had won his last two matches against Agassi, including one contest in the Davis Cup earlier this season.
"He's been playing well the whole year, so to come here and play a great match against him feels like a real achievement," Agassi told reporters.
In other third-round matches Spain's Alberto Martin beat Luis Horna of Peru 6-1, 6-3, and 15th seed Radek Stepanek knocked out Nicolas Almagro, the qualifier who eliminated Marat Safin on Wednesday, 4-6, 6-4, 6-2.
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