Mykhailo Mudryk's first goal for Chelsea and a strike from Armando Broja saw the Blues beat Fulham for only their second league win of the campaign.
Mudryk has had a mixed time at Stamford Bridge since signing for £89m in January from Shakhtar Donetsk but his first-half performance looked as though it could be a turning point in his Chelsea career.
The Ukrainian gave the away side the lead in the 18th minute when he controlled Levi Colwill's chipped cross with his chest before finishing under Bernd Leno.
Broja doubled the Chelsea lead a minute later with his first goal since October 2022 following a serious knee injury, as Chelsea moved up to 11th in the Premier League.
Fulham did not create much and their best chance came from Sasa Lukic in the second half when his shot from inside the six-yard box was well saved by Robert Sanchez.
Mudryk was withdrawn at half-time with a quad injury but boss Mauricio Pochettino was hopeful the winger would be fit enough to play at Burnley on Saturday.
This match was Mudryk's third start in a row and he looked to be benefiting from regular game time, with the 22-year-old a constant threat in the first half.
Pochettino has spoken about the need to improve Mudryk's confidence and has been playing the 'crossbar challenge' with the winger after training to help - and it certainly looks to be paying off.
At times in his 24-game Chelsea career, it has looked as though Mudryk was not confident in his decision making but everything he did in this game showed a real assertiveness as demonstrated by his clinical finish from Colwill's pass.
"Misha [Mudryk] played because he's showing in the training sessions that he deserved to be," said Pochettino.
"He was really focused and his performances in training provided us the confidence to put him on the pitch. I'm pleased for Misha and for Armando.
"Misha scored his first goal in the Premier League and for Armando after a long period out he scored again, the competition is really good for the team.
"Young people need time to settle and it has been massive change for Misha when he arrived here.
"It's not easy to settle. It's about time and being patient. It is to trust these guys, these young talented players."
Chelsea, who have 12 first-team players injured as well as striker Nicolas Jackson and defender Malo Gusto missing through suspension, were dominant in the opening half with Cole Palmer also impressing on his first league start since signing from Manchester City.
In Jackson's absence, Pochettino will have been thankful he had Broja to call on, especially when the striker took advantage of some hesitant Fulham defending to make it 2-0 soon after Mudryk's opener.
Fulham centre-back Tim Ream gifted the ball to Palmer and then kicked the Chelsea forward's pass against Broja's outstretched foot, with the ball rebounding into the net.
It was only a second Chelsea goal for 22-year-old Albanian Broja, who is working his way back to fitness after rupturing his anterior cruciate ligament in December.
Fulham's best chance of the first period came at the end of the half when a Raul Jimenez header from a corner went well wide of Sanchez's post.
Ian Maatsen, who replaced Mudryk at half-time, smacked the Fulham post as Chelsea looked for a third in the second half.
The final 15 minutes could have been much different had Lukic done better from close range when Tom Cairney's pass found him in the Chelsea area but in the end Chelsea comfortably held on.