The Bianconeri extended their lead over Roma in Serie A to four points and have a game in hand over the second-place side.
The defender has been linked with a move away from Stamford Bridge, but got himself on the scoresheet along with Willian, Pedro and Michy Batshuayi.
Richard Stearman and Andreas Weimann got the goals for the visitors, with a reply from Divock Origi unable to shake the Reds from their 2017 struggles.
Claude Puel's men will now face either Manchester United or Hull City in the final after holding out for a deserved result at Anfield.
The Spain international was returned to the starting XI and opened the scoring, with Gary Cahill's second sending the hosts eight points clear.
Antonio Conte's men did not let the absence of their star striker affect them as they eased to three points at the King Power Stadium on Saturday.
A goal 20 minutes into the encounter was enough to give the home side the advantage in after the first-leg of their EFL Cup semi-final tie.
Two goals from the Croatia international ensured the Nerazzurri carried their good form into 2017, stretching their current streak to four league wins.