Fognini guided Italy into the quarterfinals of the 2013 Davis Cup World Group, defeating Ivan Dodig in the fifth and decisive rubber against Croatia. It was the first time Italy had reached that stage since 1998. He also guided Italy past Argentina to the quarterfinals the following year, winning both singles rubbers against Juan Mónaco and Carlos Berlocq, and the doubles rubber (partnering Simone Bolelli). In the quarterfinals in Naples against Great Britain, Fognini equalled the tie at 2–2 after defeating reigning Wimbledon champion Andy Murray in a straight sets win (after defeating James Ward two days previously), proving vital to Italy making the semi-finals with an eventual 3–2 victory. This was only the second time Murray had lost a singles rubber in the Davis Cup (after his first appearance ever in 2005). In the semi-final against Switzerland he lost both his singles rubbers to Roger Federer and Stanislas Wawrinka.