But Alexandre Lacazette struck in the 93rd minute to give both sides a further taste of ICC shoot-out action, Arsenal having lost to Atletico Madrid on penalties while Chelsea had previously beaten Inter.
Maurizio Sarri has seemingly ruled out a loan move for Callum Hudson-Odoi by insisting the youngster will stay at Chelsea throughout next season.
Antonio Rudiger scored the opener for the Blues in the sixth minute but a late goal from Alexander Lacazatte in the additional time of second half sent the game into penalty shootout.
But it was Hudson-Odoi who was stamping his name on an entertaining contest, Cech quick off his line to deny the 17-year-old after he beat the offside trap.
And despite showing flashes of brilliance in pre-season, he seemingly returned to type against the Gunners with a poor penalty attempt in the first-half, which was easily saved by Petr Cech.
Chelsea continued to create chances, with Morata's header following Hudson-Odoi's cross deflected for a corner.
The Spaniard, too, doesn't yet seem closer to his preferred starting XI as he works out a way to fit all of Mesut Ozil, Henrikh Mkhitaryan, Pierre-Emerick Aubameyang and Lacazette into the team.
Inside the opening five minutes, he raced into the left channel, checked and found an unmarked Fabregas, whose shot was tipped over by Cech.
Willian flew back to London on Tuesday evening and trained alone at Cobham on Wednesday afternoon, six days after he was expected to report following an extended post-World Cup break, making him unavailable for Chelsea's third preseason match against Arsenal at the Aviva Stadium.