Chelsea dominated their hosts for most of the game but a lack of sharpness in front of goal almost cost them late on as Leicester pulled a goal back through a Jordan Ayew penalty, leading to a nervous final few minutes.
After draws against Manchester United and Arsenal before the international break, Chelsea came flying out of the traps and Jackson punished Leicester for not clearing their lines in the 15th minute.
The visitors won a long Leicester kick-out and immediately started making their way back up the pitch before Fernandez found Jackson, who took a touch before flicking the ball past Mads Hermansen with the outside of his right boot.
Chelsea continued to dominate and should have gone two up in the 54th minute, but Madueke ran ahead of the play and could not get out of the way of Palmer's close-range shot at an empty net, deflecting his effort wide.
Chelsea captain Fernandez spared his blushes with his first goal for the club in the 75th-minute.
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