The Hoops conceded cheap early goals to Xherdan Shaqiri and Rodrigo Palacio but levelled through Stuart Armstrong and Hugo Campagnaro's own goal.
Palacio pounced on Craig Gordon's error to hand Inter a half-time lead.
And the second half looked like yielding no further goals until the Swede's first goal since November.
It is a strike which keeps the tie in the balance and they play the second leg in Milan on 26 February.
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