The world number one delighted fans in the packed centre court stands with a predictably dominant display, which left Austria's Ofner little room to breathe, even in the breezy atmosphere of Rome.
Sinner won his 24th consecutive match in one hour and 40 minutes, the 24-year-old barely breaking a sweat to set up a clash with Alexei Popyrin or Jakub Mensik in the third round.
No Italian man has won at the Foro Italico since Adriano Panatta 50 years ago, and with Carlos Alcaraz out of action, Sinner is expected to go one better than last year when he lost the final to his great rival.
Such was Sinner's dominance that he had time to break into a smile when the match was stopped twice in the second set for spectator illnesses.
"I'm very happy to be back here, it's always been a very special tournament for me," said Sinner.
"I'm trying to get into a good match rhythm again, even though I've played a lot in the last couple of months... I'm very happy, and now let's see what's coming also in the next round."
It was the third win for an Italian man on Saturday, with Flavio Cobolli, who helped his country win last year's Davis Cup in Sinner's absence, beating France's Terence Atmane 7-6(1), 6-3.
Mattia Bellucci, ranked 64 in the world, is in the fourth round after a 5-7, 6-2, 6-3 win over 24th seed Tomas Martin Etcheverry.
Former winner Daniil Medvedev will begin his campaign in the third round after his match, which was scheduled to be the first on centre court, was shelved when his opponent, Tomas Machac, pulled out of the tournament with an unspecified illness.
Fourth seed Felix Auger-Aliassime suffered a shock second-round defeat at the hands of Argentina's Mariano Navone, the Canadian losing to his 44th-ranked opponent in straight sets 7-6(4), 7-6(5).