Salomon Kalou equalised for Chelsea just after half-time with a 20-yard side-foot shot but Inter went ahead again, courtesy of Esteban Cambiasso's superb strike.
Arsenal goalkeeper Jens Lehmann, who saved from Roberto Ayala and EstebanCambiasso to set up the shoot-out win, said Germany's past shoot-out success had helped himm.
As well as Essien, central midfielders Claude Makelele at Chelsea, EstebanCambiasso at Inter and now Xabi Alonso play a vital role for Mourinho tactically on the pitch.