Inter took the lead through former Manchester City striker Stefan Jovetic in the first half, with Manchester United transfer target Ivan Perisic doubling the lead soon after the break.
Perisic scored after a beauty of a run but then a stunning own goal by Kondogbia gave Chelsea the hope in the final 15 minutes but it was not enough to get them a draw.
Chelsea manager Antonio Conte says his team is working "very hard" ahead of next season's Premier League and Champions League.
Batshuayi will now directly battle record signing Alvaro Morata for the chance to be Chelsea's first-choice striker heading into the new campaign.
After Perisic's second, Inter almost made it 3-0 as he squared to substitute Joao Mario, only for the midfielder to shoot straight at Courtois.Читайте также: HTC's new standalone Vive headset is exactly what VR needs
Chelsea will now play Arsenal in the Community Shield on August 6.
Things are looking up for Inter in a major way under the tutelage of Spalletti, meanwhile, as they have beaten Lyon, Bayern and the Blues in the space of five days and topped the ICC's Singapore table as a result.
Inter should have opened the scoring in the second minute but Antonio Candreva delayed his shot and Courtois saved the winger's deflected effort well.
Goals from Stevan Jovetic and Ivan Perisic had put Inter into a commanding lead before a weird Geoffrey Kondogbia own goal gave Chelsea hope of a recovery, and Spalletti believes his players need to focus on keeping intensity levels high.
Chelsea boss Antonio Conte was sympathetic: "It can happen, can happen - this is football".При любом использовании материалов сайта и дочерних проектов, гиперссылка на обязательна.
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