Julio Cruz came off the bench to hit the winner on 79 minutes and Inter assistant boss Beppe Baresi admitted: "We knew this could be a difficult game and Lecce proved themselves to be an organised side.
"They closed down all the space and doubled up on their marking. We struggled, but we brought home the three points.
"A great team has to be able to get the result even at the end of a match like this. The whole team was a little sluggish today, but we wanted to win at all costs.
"I compliment Lecce for their performance, because we really did run some risks tonight."