A day after Andy Murray lost 6-2 6-4 to Fabio Fognini, Edmund also lost in straight-sets, although in contrast to the World No 1, the British number two battled bravely against his more experienced opponent.
Del Potro, who helped Argentina to win the Davis Cup in 2016, beat Edmund 7-5 6-4 in one hour and 46 minutes and afterwards said that he hoped he would be able to remain injury-free throughout the rest of the tournament as well as the forthcoming French Open.
“I think I'm playing better [than 2016], for sure,” said del Potro. “Last year, I was trying to win a couple of matches at this moment of the year, and now I'm beating good guys.
“I'm playing well, and I think my game can still improve week by week. It's going to be a big challenge for me to play three tournaments on clay in a row after many years.”
Edmund had been hoping to cause an upset against the Argentine and started the first-set well, breaking back to level the opening set at 5-5.
However, Del Potro targeted Edmund’s second-serve and immediately broke back, before serving out to take the first set 7-5.
Del Potro – who reached the semi-finals at Roland-Garros in 2009, but has not played at the Slam for the last four years because of injury – started the second set in superb form and quickly raced into a 5-2 lead.
He then wobbled slightly, as Edmund broke and then held his serve to raise his hopes of a fight back. But he was only able to delay the inevitable as Del Potro held his serve in the next game to progress into the last 16, where he will play seventh seed Kei Nishikori.
“It's going to be a difficult match,” said Del Potro when asked about his chances against the Japanese player.
“I think he has everything to win because he's playing so well. I'm just starting to play on this surface after my family problems. But we have never played on a clay court, so it could be an interesting match. I need to play even better than today to beat Kei.”
Del Potro will be joined in the next round by Rafael Nadal, whose opponent Nicolas Almagro was forced to retire in the first-set of their match was a knee injury.
Nadal is the overwhelming favourite to win in Rome, following his recent successes at the Monte-Carlo Masters, the Barcelona Open and the Madrid Open. He is yet to lose a clay court match this season and is widely expected to win an unprecedented tenth title in Paris next month.
It didn’t take the Spaniard long to race into a 3-0 lead before his compatriot signaled that he would be unable to continue, less than half an hour into the match on Centre Court at Foro Italico.
Nadal will now play Jack Sock for a place in the quarter-finals, after the American beat Jiří Veselý 6-4 3-6 7-6 (1).
Meanwhile, there was a shock in the women’s singles as the World No 1 Angelique Kerber lost in straight sets to the Estonian qualifier Anett Kontaveit.
The 21-year-old, who lost in the first round of every Grand Slam last year, has been enjoying something of a breakthrough season and picked up her first Top 10 win at the Porsche Grand Prix last month, as she stunned the reigning French Open champion Garbiñe Muguruza.
Her comprehensive 6-4 6-0 win in Rome was equally unexpected. “I think it does feel like an advantage in a way that I have had a few matches,” she said of battling her way through the qualification stages ahead of the opening round. “I feel comfortable on the courts here. It has been very good.”
Kerber – who has endured disappointingly early losses at Indian Wells, the Miami Open and the Porsche Grand Prix this season – was meanwhile forced to reflect on another sub-par performance.
“Everybody knows I'm not a clay court specialist,” she said during her post-match press conference.
“I was not playing good last year, as well. I had a great year, but I mean, these few weeks I was not playing good.
“I think I need one good match to get also my confidence back and then to seeing that it works, actually. Because I'm working hard, I'm trying to practice really hard and trying to improving the movement, especially on clay, because it's not 100%.
“I'm not feeling so well on this surface.”