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Simone Inzaghi's side looked to be set for a big second half to the season after dismantling champion and rival Milan in Saudi Arabia last week.
But the Nerazzurri's return to action in Serie A saw them completely out of sorts and beaten by teenager Tommaso Baldanzi's goal following a first-half red card for Milan Skriniar.
Defeats such as these may not now cost Inter in the race for Champions League qualification due to Juventus' points deduction, but any remote title hopes appear to have been quickly quashed.
Skriniar's dismissal epitomised an erratic first half from Inter, who could have trailed early on as Andre Onana saved unconvincingly from Nicolo Cambiaghi before Henrikh Mkhitaryan escaped punishment from the subsequent corner when his high boot caught Francesco Caputo's head.
Caputo continued in a bandage while Inter threatened only through Federico Dimarco, who had a volley well saved and also squared for Lautaro Martinez to stab awkwardly wide.
Skriniar, already booked, then became the second Inter man to kick Caputo in the head, and this time the foul was spotted by referee Antonio Rapuano, leading to his dismissal.
Inter showed precious little improvement after half-time and trailed when Onana, whose shaky showing had included another unorthodox stop, was beaten by a Baldanzi shot that was straight at him.
Stefan de Vrij headed against the post from inside the six-yard box but Inter proved as unimaginative in attack as they had been hapless at the back in a frustrating finale.