Maurizio Sarri’s side had slipped away from Manchester United and Arsenal in recent weeks, but goals from Gonzalo Higuain and Jorginho close the gap to two and one points respectively.
Having replaced Claudio Ranieri with Parker, Fulham showed a rare bit of fight to get themselves back into the game through Callum Chambers after Higuain opened the scoring with his third Chelsea goal.
However, Jorginho, who has been playing below his best recently, restored the visitors’ lead before the break to clinch a welcome win for Sarri.
Kepa Arrizabalaga started his first game since his Wembley dispute with the manager and atoned for an earlier error in the match with a stunning stop to deny Aleksandar Mitrovic late in the game and seal Chelsea's first away win in 2019.
Here's five things we learned from Craven Cottage
1. Chelsea play their way back into Champions League contention
Saturday’s result in the north London derby will have greatly pleased Chelsea; Tottenham and Arsenal’s draw means that they stayed within touching distance of the top four.
The win lifts them to just two points shy of Manchester United in forth and one below Arsenal in fifth with a game in hand against Brighton.
Of course, results are more important than ever at this stage of the season, but the performance on the back of their midweek win against Tottenham was a huge boost for Sarri. Having been on the brink of completely losing control of an already rogue dressing room, the manager appears to have galvanised his side ahead of their final set of fixtures.
2. Parker lifts Fulham
It was of no surprise to see the Fulham players delighted with after Chambers equalised in the first half. The goal was a result of a spirited fightback from the home side having just conceded and a show of rare unity amongst the Fulham ranks.
Every time Fulham conceded and went behind under Claudio Ranieri it effectively game over, of course apart from that freak comeback against Brighton. Parker's changes were far from revolutionary. Playing players in their preferred positions and inspiring a bit of confidence certainly went a long way to producing a much better performance.
It is, however, probably far too late to begin thinking about any miraculous escape. Southampton stayed up in 17th last season with 36 points, meaning Fulham need 19 points from an available 27, with games against Liverpool and Manchester City still to come.
3. Kepa marks return with cagey performance
Chelsea were keen to draw a line under Kepa’s appeared act of defiance in the Carabao Cup final a week ago, but since that penalties defeat against Manchester City he has been fined and dropped from the first team.
Sarri reinstated Chelsea’s number one goalkeeper for the visit to Fulham to show that it is finally time to move on from what happened at Wembley.
A fine save to keep out Aleksandar Mitrovic’s well-hit volley from the edge of the box was overshadowed by his poor handling that almost gave Fulham an early lead.
He had seemingly claimed a straightforward cross after getting above Ryan Babel, but then dropped the ball with the goal gaping. Fortunately for the goalkeeper, Babel had turned away and missed his chance to score into an empty net.
4. Sessegnon and Cairney leads old-look Fulham
After nine months of turgid football and continuous disappointment at Craven Cottage, there was a pleasant throwback watching Tom Cairney, Ryan Sessegnon and Mitrovic link up, supported by Kevin McDonald in midfield. It was a return to the simpler times and a return to the style got Fulham promoted.
Cairney often struggled to establish himself as a key player under either manager and Sessegnon was almost completely out of the picture.
The return to more trusted and crowd-pleasing players was winning back supporters, and it almost got Fulham back in the game. Cairney was especially good and his quick feet and vision often caused Chelsea problems.
Fulham will face a difficult task to retain the trio if they are relegated, but whoever buys them must use them wisely.
Sessegnon may have though he scored and rescued a point in the fourth minute of added time, but his effort was ruled out for a contentious offside.
5. Jorginho responds to critics
Sarri reiterated the importance of Jorginho for his “way of football” and challenged him to consistent after a strong performance against Tottenham in midweek.
So, how did he respond? With a goal in one of his best Chelsea performances.
After winning back possession and setting Chelsea on their way, he charged forward and opened the scoring with a fine finish from the edge of the area, his first goal since his debut on the opening weekend of the season.
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