Sarri’s side took the lead through Gonzalo Higuain before Calum Chambers equalised at Craven Cottage.
In an incident-packed first half, the much-maligned Jorginho restored Chelsea’s lead with his first goal since the opening weekend of the season.
Chelsea were indebted to Kepa for a series of superb saves that preserved their lead after the break, lifting the sixth-placed Blues within two points of fourth-placed Manchester United, with a game in hand.
Sarri had dropped Kepa for Chelsea’s 2-0 win over Tottenham on Wednesday as punishment for the Spaniard’s refusal to be substituted during last weekend’s League Cup final defeat against Manchester City.
But Sarri had insisted Kepa remained his “first choice” and the world’s most expensive keeper returned in place of Willy Caballero after his one-game demotion.
Revealing he didn’t tell Kepa he had been recalled until a team meeting on the day of the game, Sarri said: “He played very well. It was a normal decision. He made a big mistake, he paid for it. Now the situation is closed.
“I can kill him, but I don’t think it is right. With another man I could have done it in another way, but I know him well.
“He has a good mentality. His behaviour during the week was very good.
“Kepa is a man. He was able to react very well, as we have seen today.”
Sarri believes Chelsea’s revival this week, coupled with Tottenham’s poor form, has made the top-four chase even tighter.
“We had a great opportunity today. Now we are only two points from the top four. We have to fight to the last minute of the last match,” he said.
“We are fighting. In the last four matches I think we did well.”
Despite an improved display in caretaker manager Scott Parker’s first game following the midweek sacking of Claudio Ranieri, second-bottom Fulham have lost eight of their past nine league games and sit 10 points from safety.
Kepa’s return almost started in embarrassing fashion when he made a complete hash of catching Kevin McDonald’s cross in a swirling wind, the ball slipping through his grasp as he was challenged by Ryan Babel.
It would have been an open goal for Babel, but the Fulham winger was slow to react and Kepa scrambled back to dive on the ball.
Chelsea made the most of their escape to take the lead in the 20th minute.
Willian’s pass picked out Cesar Azpilicueta’s run down the right and Chelsea’s captain whipped over a cross that Higuain met with an instinctive volleyed finish.
Despite an improved display in caretaker manager Scott Parker’s first game following the midweek sacking of Claudio Ranieri, second-bottom Fulham have lost eight of their past nine league games and sit 10 points from safety.
Kepa’s return almost started in embarrassing fashion when he made a complete hash of catching Kevin McDonald’s cross in a swirling wind, the ball slipping through his grasp as he was challenged by Ryan Babel.
It would have been an open goal for Babel, but the Fulham winger was slow to react and Kepa scrambled back to dive on the ball.
Chelsea made the most of their escape to take the lead in the 20th minute.
Willian’s pass picked out Cesar Azpilicueta’s run down the right and Chelsea’s captain whipped over a cross that Higuain met with an instinctive volleyed finish.
Kepa to the rescue
It was Higuain’s third goal in eight games since the Argentine striker joined on loan from Juventus in January.
Kepa redeemed himself with an acrobatic save to keep out Aleksandar Mitrovic’s volley from Ryan Sessegnon’s cross.
It was Higuain’s third goal in eight games since the Argentine striker joined on loan from Juventus in January.
Kepa redeemed himself with an acrobatic save to keep out Aleksandar Mitrovic’s volley from Ryan Sessegnon’s cross.
But from the resulting corner, Chelsea were punished for an awful piece of defending as Fulham grabbed a 28th-minute equaliser.
Chambers was left totally unmarked when Fulham took the corner quickly, Babel picking out his team-mate at the far post for a well-taken finish.
Three minutes later, Eden Hazard was the catalyst for Chelsea’s second goal with an incisive run into the Fulham area, the Belgian laying the ball back to the Jorginho, who guided a superb strike into the top corner from 18 yards.
Fulham were finding it impossible to stifle Willian and Azpilicueta down the right and the pair combined to tee up Higuain, whose powerful strike drew a brilliant one-handed save from Sergio Rico.
Exploiting the space left by Fulham’s creaky defence, Hazard and Willian both tested Rico with low drives soon after the restart.
Even with the perennially inconsistent David Luiz left on the bench, there were still moments of uncertainty from Chelsea at back.
Mitrovic blasted just over from 20 yards and Tom Cairney’s long-range effort forced a good stop from Kepa.
Joe Bryan forced Kepa to make another solid save and the Spaniard was firmly back in Sarri’s good graces by the time he repelled Mitrovic’s late header.
Sessegnon thought he had equalised in stoppage-time, but the winger’s goal was ruled out for offside.
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