The former Spurs midfielder slotted home from the edge of the area after Romelu Lukaku’s lay-off with about 20 minutes remaining.
The Dane additionally hit the bar with a force from 25 yards before Lukaku sealed the win with a penalty in added time.
The 2nd leg takes place at the San Siro next Thursday (27 January).
Since becoming a member of Antonio Conte’s side Eriksen had performed 137 minutes throughout five fits but failed to register a goal or assist.
However, on a night time that Inter managed – limiting the hosts to just one off-target effort – his calm finish into the backside right-hand corner past Plamen Iliev confirmed his quality.
Manchester United loanee Alexis Sanchez additionally played for Inter alongside former Chelsea winger Victor Moses and Ashley Young came off the bench as a second-half substitute.