Delbonis broke Lorenzi's serve to start the decisive set and held on to close the match in 2 hours, 6 minutes after converting on his second match point. He jumped and punched the air after sending a winner down the line past the outstretched arms of Lorenzi.
Delbonis celebrated a nearly perfect week in which he also reached the semifinals in the doubles tournament.
"To tell you the truth, I have no words," Delbonis said. "I played well match after match. It was a great result in the end."
With the victory at the ATP 250 tournament in Sao Paulo, Delbonis will move to 45th in the ATP rankings, a career best.
The 32-year-old Lorenzi, ranked 114th, had never advanced past the quarterfinals of an ATP singles tournament. He reached the Sao Paulo final by beating top-seeded German Tommy Haas, who retired in the semifinals because of a right shoulder injury while losing in the second set.
"It's a shame I wasn't able to win," Lorenzi said. "But hopefully I'll be back next year to try again."
The Italian won the first set on Sunday after breaking Delbonis' serve at 3-3, but the hard-hitting Argentine started serving well and was never broken again, finishing with 12 aces and no double faults.
It was the first time since 2007 that the Brazil Open wasn't won by a Spanish player. Argentine Guillermo Canas lifted the trophy that year, and after that the tournament was won by Spaniards Almagro, Tommy Robredo, Juan Carlos Ferrero and Rafael Nadal.
Nadal decided not to defend the clay-court title this week. He chose to play in the first Rio Open, which he won last week.
In the doubles final on Sunday, Guillermo Garcia-Lopez of Spain and Philipp Oswald of Austria beat Juan Sebastian Cabal and Roberto Farah of Colombia 5-7, 6-4, 15-13. The Colombians, No. 5 in the world and second-seeded in Sao Paulo, won the Rio Open last week.
Delbonis reached the semifinals of the doubles tournament playing with countryman Facundo Bagnis, losing to the eventual champions.