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.
"There is always things to improve, but it is not the right time to say I'm not happy with one thing or another.
"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.
There was also a win for Japanese seventh seed Kei Nishikori, with Asia's best player defeating David Ferrer 7-5, 6-2.
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).