The 22-time Grand Slam champion had not played a competitive match since January but eased past the 62nd-ranked Cobolli in 85 minutes to reach the second round.
The former world number one has seen his ranking slip to 644 after missing all of the 2023 season following the Australian Open. His comeback at the start of this year hit a stumbling block when he felt a hip injury flare up in Brisbane.
For Nadal, a 12-time winner in Barcelona, it was his first appearance on clay since he won the French Open almost two years ago, but the Spaniard was keen not to get ahead of himself.
Stefanos Tsitsipas, last week's Monte Carlo Masters champion, said earlier this week he wouldn't be surprised to see Nadal to reach the final on a court named after him.
"Today to say that I am favourite I think is stupidity, Tsitsipas knows that it's not the case," said Nadal, who turns 38 in June.
"I understand what he says as respect for what I have done in this tournament. Everybody knows I am not favourite to win a tournament."
"I didn't have the slightest idea if I was favourite today, I know tomorrow I will not be," added Nadal, who plays fourth seed Alex de Minaur for a place in the last 16.
"But it doesn't matter, I will go out and play and it will be an experience against a top-level player."
After a double fault to fall 30-0 behind Nadal found his rhythm, with Cobolli intimidated by the fervent support for the Spaniard on the court named after him.
Nadal converted his third break point in the fourth game for a 3-1 lead, with Cobolli surviving four more to hold at 4-2 down. The Spaniard broke again to claim the set in 43 minutes, clenching his fist in celebration.
Cobolli handed Nadal a break for 2-0 in the second set with two more unforced errors but finally put some pressure on Nadal's serve in the third game to break back. However, Nadal broke again for 3-1 after Cobolli's third double fault and served it out to triumph.
"It was a good start - when you return you can't get rid of the doubts in one day, above all, on a physical level," Nadal told TVE.
"Within what it could be, it was a good first round. He made mistakes and I think I played the game that I had to play."
