Morata came off the bench in the friendly defeat to Bayern Munich in midweek, but the £60m striker will be on the pitch from the opening whistle in his second match in a Blues shirt.
Minutes later N'Golo Kante saw his shot blocked after good play from Marcos Alonso and new signing Alvaro Morata.
But Chelsea manager Antonio Conte struggled to see his men carve open many chances on goal, giving the sense that without key men such as Eden Hazard, Pedro and Diego Costa, their other options weren't up to the task.
Inter were firmly in control until an wonderful own goal gifted Chelsea a way back into the match in the 74th minute when Geoffrey Kondogbia inexplicably lofted an overhit back pass over Daniele Padelli from near the halfway line.
With time fast running out, Michy Batshuayi thought he had restored parity for Chelsea but his goal was disallowed for offside.
Eden Hazard and Pedro are injured and that has forced Antonio Conte to find a new left winger for the team.
And Conte accepted Morata has work to do on his fitness, with the Community Shield against Arsenal set to get Chelsea's campaign under way on August 6.
It overshadowed what had otherwise been an impressive performance by Inter, and in particular Manchester United target Perisic.
Goals from Stevan Jovetic and Ivan Perisic gave Inter the win, but the game will be remembered for an own goal from Geoffrey Kondogbia, who netted an own goal from 45 yards.
Substitute Joao Mario could have made it three on the hour when Perisic unselfishly teed him up, but Courtois saved with his legs before Kondogbia's memorable impact.
With Chelsea 2-0 down and seemingly out of the contest, the Frenchman threw the English side a lifeline in the most freakish fashion, lobbing his own goalkeeper Daniele Padelli from all of 40 yards with a miscued back-pass.