Spain international Kepa was dropped for the midweek win over Tottenhamafter refusing to be substituted in the Wembley defeat to Manchester City, but he returned at Craven Cottage as Chelsea moved back to within two points of the top four.
Fulham, playing their first game since Claudio Ranieri was sacked and replaced by interim boss Scott Parker, put up a scrap at times and even cancelled out Gonzalo Higuain's opener when Calum Chambers equalised.
But Jorginho put Chelsea back in front and, despite Fulham's noble efforts, the Blues managed to hold on, leaving Parker's men 10 points adrift of safety.
Kepa almost embarrassed himself 18 minutes into his return, dropping a routine cross right in front of Ryan Babel, but fortunately he was able to pounce before the Netherlands international could punish him.
Shortly afterwards, Chelsea capitalised on that let-off – Higuain steering Cesar Azpilicueta's low cross in with a first-time finish.
Fulham levelled seven minutes later when an unmarked Chambers met Babel's cross following a short corner with a controlled finish at the back post.
But Chelsea restored their lead in the 31st minute, as Eden Hazard teed up Jorginho on the edge of the box, who found the top-right corner.
Proceedings continued to be open after the break – Willian and Aleksandar Mitrovic both going fairly close within 15 minutes of the restart.
Kepa rescued Chelsea with a fine flying save to parry Mitrovic's header, securing victory and a hint of redemption, before Ryan Sessegnon saw an injury-time leveller correctly ruled out for offside.
Race for top four heats up
Everything points to the battle for the third and fourth Champions League spots being quite thrilling towards the end of the season. Just five points now separate Spurs in third and sixth-place Chelsea, meaning there could be plenty more twists and turns in the final weeks.
Hazard leads Chelsea once again
It was not his best display ever, but Hazard was certainly a leading light for Chelsea, tormenting Denis Odoi constantly before his late withdrawal, while he set up Jorginho's winner with a good run and pass. That made him only the third Chelsea player to both score and assist 50 goals in the Premier League.
