The Spaniard had been kept out of competitive tennis since June 28 by a knee injury and then, most recently illness, before making his comeback in doubles action in Chile.
But, following his victory alongside Juan Monaco on Tuesday, Nadal looked a little rusty in the early stages of his second-round tie against Delbonis, winning only one point in the first two games as he was broken early.
However the former world number one recovered impressively on his favoured clay surface, breaking in the fourth game to get back on level terms.
He dropped just one more game as he wrapped up the opening set in 47 minutes in front of a sell-out crowd of 4,500 at the temporary stadium.
Nadal, who had not featured since being stunned by Lukas Rosol in the second round at Wimbledon last summer, then breezed through the second set.
"The beginning was tough and Federico played at a very high level," the 11-time grand slam winner said afterwards. "I ran a lot and I'm happy because the knee held up well.
"I feel happy to be playing singles again. It's been an important day for me."