Antonio Conte handed a first Chelsea start to Alvaro Morata and he was soon in the thick of the action when nearly latching on to a long ball, but Inter also started brightly with Thibaut Courtois and Gary Cahill having to get in the way to prevent the Italian outfit from going ahead.
After a fast opening, the game finally settled down with only Michy Batshuayi getting any kind of a shot on goal before the half-hour mark, but Chelsea soon began to press forward with David Luiz seeing a goalbound header cleared and Willian firing a deflected effort just over the bar.
Luiz also drilled a free kick marginally wide from over 30 yards out, with Batshuayi the next to go close when seeing a shot blocked after a mistake from Padelli.
It appeared that the two teams would go into half time on level terms but in the second minute of injury time, Cesar Azpilicueta was harshly adjudged to have pushed Jovetic in the area and although Courtois saved the former Manchester City attacker's penalty, the rebound was converted.
While Chelsea felt hard done by going into the break, they were fortunate to avoid falling further behind straight after the restart when Jovetic found the back of the net from close range, but he was wrongly adjudged to have scored from an offside position.
The Blues should have made the most of that reprieve when Cesc Fabregas teed up Batshuayi inside the penalty area, but he struck his effort wide of the post when he probably should have scored.
It took just three more minutes before Inter doubled their advantage through Perisic, who picked up the ball from Jovetic before finding the far corner of Courtois's net, despite the angle being against him.
Chelsea would have fallen further behind had it not been for Courtois denying Joao Mario with his legs, and while that save kept Chelsea in the contest, no-one could have foreseen how they would halve the deficit with 16 minutes remaining.
Kondogbia was 45 yards from his own goal but while presumably attempting a back pass, he managed to send the ball over Padelli and into the top corner of his own net.
It was a goal which came against the run of play but Chelsea built on their good fortune, with Cahill heading at Padelli from a corner and Charly Musonda forcing a decent save from the goalkeeper low down to his right.
Chelsea should have equalised with three minutes left when Batshuayi finished well from Fabregas's pass, but the officials again made a mistake in adjudging an attacking player to have been offside.
In added-on time, Cristian Cuevas was denied by Padelli - who had enjoyed an excellent match for Inter - and Luciano Spalletti will be delighted after his new team were able to hang on to claim a notable victory over the English side.