The Giallorosse - defending champions in the competition - had Italy international Giugliano to thank as they finally made their superiority count midway through the second half; the midfielder curling home from a free-kick.
"I'm pleased to have scored and to have helped secure the win," Giugliano said.
"It's a really important result for us. It means we can take on the second leg, in front of our own fans, with even more belief and determination. Winning builds our confidence for the league as well."
Alessandro Spugna's side will thus return to Tre Fontane for the second leg with a lead to play with, as they look to make it to the final of the competition for the second season in succession.
Juventus beat AC Milan 6-1 in the first leg of the other semi-final.
"Credit to Empoli because they did well and made it tough for us - especially towards the end," Spugna noted.
"We had a fair amount of chances, especially in the first half where we should have taken advantage of that - and if we had we would be sitting here talking about a different game.
"But the great thing is we have come away with a win and a clean sheet, which bodes well for the return game."
See more photos from the match in our gallery below!
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