The Londoners now need to match Inter’s result at home to PSV Eindhoven on 11 December to reach the last 16.
“We have big respect for Barcelona, but we have belief that we can win.”
Barca have not lost at home in the Champions League since 2013.
Spurs knew anything but a win over Inter would see them go out of the competition.
Harry Winks struck the bar and Jan Vertonghen headed wide as Spurs pressed but it took the introduction of Eriksen to make the crucial breakthrough.
The Dane was the beneficiary of good work by Moussa Sissoko and Dele Alli to score at the far post with 11 minutes left.
Inter had opportunities, with Spurs keeper Hugo Lloris saving from Ivan Perisic, but the hosts closed out the win and travel to Spain with their destiny in their own hands.