The midfielder fired home a deflected equaliser in the closing minutes to cancel out Mauro Icardi's header and extend the Nerazzurri's winless run in Sardinia
The Nerazzurri came into the match on the back of four wins and a draw from their opening five games and the fourth-placed side had only lost to Cagliari twice since 1995.
Half-time substitute Mauro Icardi scored the game’s first goal with 15 minutes remaining, but Radja Nainggolan struck even later to earn the home side a point at the Stadio Nereo Rocco.
The hosts made only two changes from Wednesday’s 1-1 draw at Livorno as Albin Ekdal and Nene missed out in favour of Matias Cabrera and Mauricio Pinilla.
Inter picked up a commendable win over Fiorentina in their last fixture, but coach Walter Mazzarri still opted to rotate his players. Jonathan, Hugo Campagnaro, Saphir Taider and Rodrigo Palacio all took places on the bench, while Rolando, Alvaro Pereira, Mateo Kovacic and Ishak Belfodil started.
The share of possession in the opening exchanges was even, but Inter looked considerably more dangerous going forward.
Belfodil did well down the right just before the 10th minute as he cut a pass back to Fredy Guarin, but Agazzi tipped his deflected effort over the bar.
Agazzi was Cagliari’s saviour again 23 minutes in as he got down to keep Belfodil’s header out after the Algerian connected with Yuto Nagatomo’s cross.
There was little Agazzi could do moments after the half-hour mark as Ricky Alvarez cut in from the right and fired a dipping shot towards the far corner, but the Argentinian’s effort flew just over the crossbar.
The second period took a while to get into a steady flow, but Inter were convinced they had taken the lead in the 61st minute.
Half-time substitute Icardi headed Pereira’s cross back across goal, with the Uruguayan turning home after David Astori had cleared the initial effort, but the referee ruled it out for a foul by Kovacic.
Pereira soon had another chance, however. Belfodil crossed excellently to the back post and the former Porto man met it with his head, but he could only put it wide.
Agim Ibraimi missed a glorious chance to break the deadlock with a volleyed effort from close range, and he was punished soon after as Inter took the lead.
Nagatomo cleverly got behind the Cagliari defence and played the ball across the face of the goal for Icardi to head home, giving the home side less than 15 minutes to find an equaliser.
Inter looked destined to leave Sardinia with three points for the first time since 2010 but, with less than 10 minutes to play, Nainggolan cut in from the left and saw his powerful strike deflect past the helpless Samir Handanovic, rescuing a point for Cagliari.