Three-time French Open quarter-finalist Almagro -- he lost all three to Nadal -- was unable to continue after 24 minutes while trailing his compatriot 3-0 in the first set.
It was a 50th win for Nadal in Rome and he is on a hot streak after sweeping the honours on clay at Monte Carlo, Barcelona and last weekend in Madrid.
"I am happy with almost everything, I am playing well. I won a lot of matches this year," said the fourth seed, who next faces either Jack Sock or Jiri Vesely as he builds up to Roland Garros.
"There is always things to improve, but it is not the right time to say I'm not happy with one thing or another.
"I am happy with everything. But always there is the motivation to keep going and to keep improving something."
Nadal though was distressed to see Almagro injured.
"It's difficult to say something because we need to wait a couple of days. It's difficult to see what's going on now just after what happened," he said.
Joining Nadal in the next round was Japanese seventh seed Kei Nishikori, winner over Spain's David Ferrer 7-5, 6-2.
In women's play, world number one Angelique Kerber crashed out, the top seed beaten 6-4 6-0 in the second round by Anett Kontaveit of Estonia.
The German's 56-minute knock-out came two days after she was confirmed at the top of the WTA rankings, displacing Serena Williams after making it to the third round at last week's Madrid Open.
The defeat demonstrated more of the patchy and inconsistent form which the 29-year-old cannot seem to shake off since starting to duel with Williams at the top of the rankings last season.
second seed Karolina Pliskova beat Lauren Davis 6-1, 6-1, Madrid winner Simona Halep started with a win over Germany's Laura Siegemund 6-4, 6-4 and eighth seed Elina Svitolina put out Alize Cornet 6-4, 7-6 (13/11).