Spain international Kepa was dropped for the midweek win over Tottenham after 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.
What does it mean? 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.
Odoi out of his depth
Frequently targeted by Chelsea, the right-back had no answer to Hazard and even played himself into danger on a few occasions.
Key Opta Facts
50 - Eden Hazard is the third Chelsea player to both score and assist 50 Premier League goals (81 goals, 50 assists) after Frank Lampard and Didier Drogba. Showtime. pic.twitter.com/jnwOGe5vIE— OptaJoe (@OptaJoe) March 3, 2019
- Chelsea are unbeaten in 18 Premier League games against Fulham (W11 D7) – only against Tottenham (28 games between 1992 and 2006) have they had a longer unbeaten run versus an opponent in the competition.
- Fulham have become the first side to lose 10 London derbies in the top flight in a single season.
- Chelsea scored their first away league goal in 2019 – they were the 91st of the 92 English league clubs to do so, leaving only Huddersfield Town without one.
- Fulham's Calum Chambers' last four Premier League goals have been scored under four different managers (Arsene Wenger, Steve Agnew, Claudio Ranieri and Scott Parker).
- Eden Hazard has been involved in at least one goal in all four of his Premier League appearances against newly-promoted sides for Chelsea this season (3 goals, 3 assists).
- Fulham have lost more matches than any other side in the top-five European leagues in all competitions during 2019 (9).