A first half own goal proved to be all that separated the two sides in the first leg, after Riccardo Marchizza's dangerous low cross was turned into his own net by an unfortunate Nerazzurri defender.
Alberto De Rossi's side had further opportunities to extend their lead throughout the contest, but will now have to ensure they do in a professional job in the second leg in Milan if they are to reach the final of the competition.
"It was a great game," De Rossi said. "Our first-half display was one to remember and we kept that up in the first 25 minutes of the second half.
"One slight criticism would be that we could have scored a second goal, given how we were playing. This victory only brings us so far though, as we’ll need to really dig in when we go to Milan if we’re going to reach the final. We got a bit stretched towards the end of the game and we need to get back that rhythm we had before the break."
He added: "We really want to get to the Coppa Italia final. It’d be a great feeling for a fantastic group of lads.
"Now we’ll go over the mistakes we made, and there weren’t many, before turning our attentions to the league. We’ve dropped off a bit there so we need to try and work our way up the table."
See some of the best images from the match in the gallery below.
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