Central defender Antonio Rudiger, signed from AS Roma early in July, came on for his Chelsea debut with more than 30 minutes remaining, while attackers Jeremie Boga and Charly Musonda replaced Morata and Willian, respectively, in the 65th minute.
Inter found the breakthrough in the third minute of first-half stoppage time when Jovetic was awarded a penalty after being fouled in the box.
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.
Alvaro Morata started his first game for the Blues following his £60m move from Real Madrid and he looked lively throughout despite not scoring.
Michy Batshuayi thought he had leveled matters for Chelsea in the 88th minute, but the striker's effort was flagged offside.
The Blues have a little more than one week to prepare for their FA Community Shield matchup against Arsenal on August 6 at Wembley Stadium, while Inter will face Spanish sides Villarreal and Real Betis before their Serie A season gets underway on August 20 against Fiorentina.
It overshadowed what had otherwise been an impressive performance by Inter, and in particular Manchester United target Perisic. "We know it will be hard next season and we will try and avoid what happened to Mourinho's side at the start of 2015".
Inter led by two goals from the impressive Ivan Perisic and Stevan Jovetic, before what was supposed to be a routine backpass from substitute Kondogbia looped over his own goalkeeper and nestled into the top corner from fully 40 yards, stunning the crowd of over 32,000.