The world number one, who is playing his first tournament since reaching the final of the Australian Open, broke six times as he cruised past his fellow Spaniard.
“When you get injured in the final of a Grand Slam and stop for two-and-a-half weeks it’s not easy to come back," said Nadal, who was sporting elastic tape across his lower back.
"The back is still bothering me a little bit. But I am happy with my decision to be here."
Fognini, ranked at a career-high 14th in the world after a good start to the Latin American claycourt swing, will play Alexandr Dolgopolov for a place in the semis after the Ukrainian edged Facundo Bagnis of Argentina 6-7(4) 6-2 7-6(4) in a battle that lasted over two-and-a-half hours.
Meanwhile, at the Delray Beach Open, a hip injury forced third seed Kei Nishikori to retire from his second round match in Florida.
The world number 15 from Japan, coming off his win in Memphis on Sunday, his fourth ATP career title, lasted only six games against Teymuraz Gabashvili of Russia.
Gabashvili was leading 4-2 when Nishikori called it a day due to a painful left hip flexor. He later withdrew from next week's Acapulco event.
"I tried to play, but if you're not 100 per cent, it's tough," Nishikori said.
"I couldn't do anything today. It's going to take some time to recover. It's shocking this happened, especially since I've been playing well."
In a match of fluctuating fortunes, American Isner had four match points in the 10th game of the third set before Sela, who is ranked 75th in the world, recovered to hold serve.
Buoyed by that escape, Sela led 5-2 in the tiebreak before Isner won the final five points of the match, closing it out with a forehand winner.
"It puts a lot of stress on me playing matches like that. It seems I always do it but I'm glad to get through," said Isner, who has a perfect 5-0 record in three-set matches this year.
"I wish I didn't have to dig so deep... I think he (Sela) may have got a little nervous (in the tiebreak)."
Seventh seed Marin Cilic of Croatia had a more easier outing, beating American Ryan Harrison 6-3 6-4.
In Thursday's late game, American Rhyne Williams outlasted Marcos Baghdatis of Cyprus 6-7 (7) 6-4 6-2.
Rio de Janeiro Open results
1-Rafa Nadal (Spain) beat Albert Montanes (Spain) 6-1 6-2
Alexandr Dolgopolov (Ukraine) beat Facundo Bagnis (Argentina) 6-7(4) 6-2 7-6(4)
Delray Beach International results
Rhyne Williams (U.S.) beat Marcos Baghdatis (Cyprus) 6-7(7) 6-4 6-2
7-Marin Cilic (Croatia) beat Ryan Harrison (U.S.) 6-3 6-4