Nadal lost his serve in the first game but quickly hit back, taking command of the match and winning the first set in 50 minutes at the Pacific resort city of Vina del Mar.
The French Open champion seemed surprised when Delbonis took a 2-0 lead, but with some fierce shots he put things in their place.
The former world number one began to vary his game and showed greater mobility in a one-sided second set which he wrapped up in 38 minutes.
"I feel happy to be playing singles again. It's been an important day for me," Nadal told local television after the match.
"Thanks for supporting me. I'd never dreamed of a comeback like this," he added in front of an ecstatic crowd.
"It was a tough start. Federico played really well and forced me to run a lot".
Nadal took advantage of four of his eleven chances to break Delbonis's serve.
The Spanish left-hander had been out with a knee injury since losing to Czech Lukas Rosol in the second round at Wimbledon in June.
"I'm happy the knee responded well," Nadal added.
In the quarter finals, Nadal will play against the winner of Thursday's match between Spaniards Albert Montanes and Daniel Gimeno-Traver.
The 26-year-old, whose planned end-of-year return was delayed due to illness, will now compete on his favourite clay surface at three Latin American events this month.
Nadal will compete at the Brazil Open in Sao Paulo next week and the Mexico Open in Acapulco from February 25.
ATP Vina del Mar
1-Rafa Nadal (Spain) beat Federico Delbonis (Argentina) 6-3 6-2
8-Carlos Berlocq (Argentina) beat Santiago Giraldo (Colombia) 7-5 4-6 6-4
Guillaume Rufin (France) beat 2-Juan Monaco (Argentina) 7-6(3) 6-4
6-Paolo Lorenzi (Italy) beat Gianluca Naso (Italy) 6-1 6-4
7-Daniel Gimeno-Traver (Spain) beat Joao Sousa (Portugal) 6-4 4-6 6-1
5-Albert Ramos (Spain) beat Rogerio Dutra Silva (Brazil) 6-4 6-1
8-Benoit Paire (France) beat Steve Darcis (Belgium) 4-6 7-6(11) 6-4
Jarkko Nieminen (Finland) beat 5-Nikolay Davydenko (Russia) 6-3 7-6(8)
Round 1 Michael Llodra (France) beat Kenny De Schepper (France) 6-3 6-3
Tatsuma Ito (Japan) beat Edouard Roger-Vasselin (France) 3-6 7-6(5) 7-5
6-Julien Benneteau (France) beat Adrian Ungur (Romania) 6-3 4-2 (Ungur retired)
Arnau Brugues (Spain) beat Mikhail Kukushkin (Kazakhstan) 6-7(5) 6-3 7-6(3)
7-Viktor Troicki (Serbia) beat Lucas Pouille (France) 6-4 7-5
3-Mikhail Youzhny (Russia) beat Igor Sijsling (Netherlands) 6-3 6-2
Round 1 Ivan Dodig (Croatia) beat Benjamin Becker (Germany) 6-2 7-6(3)
6-Marcos Baghdatis (Cyprus) beat Tobias Kamke (Germany) 6-7(6) 6-2 6-4
Robin Haase (Netherlands) beat Antonio Veic (Croatia) 2-6 6-3 6-3
Flavio Cipolla (Italy) beat 8-Lukas Lacko (Slovakia) 1-1 (Lacko retired)