Kyogo Furuhashi showed great composure to slide in his first goal in the competition to ignite a rowdy Celtic Park early on.
However, indecision in the home defence was punished midway through the first half as Matias Vecino was afforded space to glance in a header.
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Brendan Rodgers’ side thought they’d snatched a late winner through Luis Palma only for VAR to intervene, however Celtic’s anguish would grow further as the Italians dramatically struck with just seconds left.
With Atletico Madrid beating Feyenoord 3-2 in Spain, it means Celtic, who have now not won at home in the Champions League for 10 years, sit bottom of Group E with no points after two games ahead of a double header against the Spaniards.