It looked as though the Nerazzurri would pick up their first win of the season when first-half goals from Ivan Perisic and Stefan de Vrij put them into a deservedly commanding lead at half time, but Torino fought back in the second half.
Inter are also stuck on just one point after two games, but the early signs looked good in their quest to bounce back from last weekend's shock defeat to Sassuolo and the hosts were ahead after only seven minutes.
Mauro Icardi's low pass into the box from the right picked out Perisic, who had peeled away from his marker and swept a clinical first-time finish past the keeper with aplomb.
Inter continued to dominate the possession and territory in the first half and eventually doubled their lead shortly after the half-hour mark when De Vrij glanced Politano's wicked free-kick delivery past the keeper.
Matias Vecino had the chance to kill the game off once and for all moments later, but he was thwarted by Sirigu and Torino began to show signs of their impending fightback towards the closing stages of the first half.
Falque was the provider when Torino did pull a goal back 10 minutes into the second half, sending a long ball forward for Belotti, whose delicate first touch took him past an overly-committed Handanovic and left him with a simple finish into the empty net.
Suddenly the visitors were looking a lot more dangerous, and the equaliser arrived with just over 20 minutes remaining when Meite picked up a loose ball on the edge of the area before seeing his deflected strike squirm past Handanovic and creep into the bottom corner.
Things could have been even worse for the hosts shortly afterwards when Torino came forward again, but this time Belotti's strike was blocked before it could test the keeper.
An end-to-end closing 20 minutes followed, with Belotti drilling another strike narrowly over before Perisic fired wide at the other end just moments later.
Inter had nowhere near the degree of control over the game that they had enjoyed in the first half, though, and they needed Handanovic to deny Adem Ljajic before Belotti put another effort narrowly wide from the resulting corner.
Perisic looked the most likely to make something happen for the home side during the closing stages and nodded one effort over the bar, while Icardi also squandered a good sight of goal moments later.
It made for an action-packed end to the game and there was still time for Belotti to come close once more, but the closest either side came to a winner arrived in the 92nd minute.
Perisic found space to shoot just outside the area and unleashed a powerful strike which looked destined for the top corner, but Sirigu pulled off a stunning stop to claw it away and earn his side a point.
Inter are now winless in their last three Serie A games at San Siro and will renew their search for a first win of the campaign against Bologna next weekend.
INTER MILAN (3-4-3): Handanovic; D'Ambrosio, De Vrij, Skriniar; Vrsaljko (Balde 72'), Vecino, Brozovic, Asamoah (Henrique 66'); Politano (Martinez 92'), Icardi, Perisic
TORINO (3-5-2): Sirigu; Izzo, N'Koulou, Moretti; De Silvestri, Soriano (Ljajic 61'), Rincon, Meita, Ansaldi (Aina 22'); Falque (Lukic 88'), Belotti