Three-time French Open quarter-finalist Almagro -- he lost all three to Nadal -- was unable to continue after just 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 titles 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 Jack Sock as he builds up to Roland Garros where he will be chasing a 10th title.
"Always there is the motivation to keep going and to keep improving something."
Nadal though was distressed to see Almagro injured who he also helped from the court.
"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 Swiss third seed Stan Wawrinka, who beat Benoit Paire 6-3, 1-6, 6-3 while Canadian fifth seed Milos Raonic ended the Rome run of 39-year-old Tommy Haas, 6-4, 6-3.
Madrid finalist Dominic Thiem started his week with a win over Pablo Cuevas 7-6 (7/4), 6-4. Sock defeated Jiri Vesely 6 -4, 3-6, 7-6 (7/1).
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.
Second seed Karolina Pliskova beat Lauren Davis 6-1, 6-1, Madrid champion 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).
French Open champion Garbine Muguruza of Spain had to recover to post a 2-6, 6-2, 6-1 win over Latvian qualifier Jelena Ostapenko.
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