The Blues were quick off the mark, and Alvaro Morata nearly gave them a first-minute lead but an outstretched leg from Samir Handanovic came to Inter’s rescue.
The deadlock was to be broken not before Morata thought he had done so on four minutes when he headed over the head of Handanovic but was correctly ruled for offside.
Spaniard Pedro was perfectly placed to side-foot home the opener off a cross-field pass from Morata after Antonio Candreva failed to clear his lines properly, 1-0.
Inter’s first shot in anguish found Candreva out wide and ran towards goal, but his shot failed to connect with Mauro Icardi as it skewed wide.
Callum Hudson Oddoi found space out on the left and tried to cut inside for a shot which he managed to do in the end, though it failed to trouble Handanovic who saved easily.
The Nerazzurri were level after Icardi won possession in the middle and set-up Roberto Gagliardini to beat substitute goalkeeper Willy Caballero with a cool finish on 48 minutes.
Chelsea were struggling to get in the same rhythm as the first half, and Inter threatened to get a second but a long range shot from Gagliardini failed to beat Caballero.
Frenchman Tiemoue Bakayoko showed his striking instinct when he turned inside the box to get the best out of Handanovic who got down to tip away his shot before gathering at the second attempt.
Played in sweltering heat, water breaks was needed in both halves but the intensity of the game itself never dropped.
Handanovic pulled off another heroic save to keep out Emerson’s curler from finding the top corner nine minutes to the dreaded penalty shoot-out sequence.
In added time, Martinez almost found the winner for Inter when a cross from Danilo Dambrosio found his path but his first-time volley produced his countryman to deflect for a corner.
As neither side found a winner, penalties was to decide. Inter took first and Andrea Ranocchia send Caballero the wrong way, with Chelsea’s new signing Jorginho doing the same at the opposite end.
The pattern continued until a miss from Milan Skriniar handed the advantage to the English who converted all their spot kicks with Cesar Azpilicueta converting the final kick for a 5-4 win.