Pedro opened the scoring as early as the fourth minute and, although Fulham battled away gamely on Claudio Ranieri's return to Stamford Bridge, they could not find an equaliser and Loftus-Cheek made sure of the three points for his side during the closing stages.
Chelsea find themselves back in third place in the Premier League standings after Tottenham Hotspur's defeat in the North London derby, but Fulham remain bottom despite a positive showing against their neighbours.
However, the Cottagers' early work was quickly undone as N'Golo Kante dispossessed Jean Michael Seri before advancing into the penalty area to tee up Pedro, who cut inside a defender before finding the bottom corner from close range.
Fulham began to look there for the taking as Chelsea had joy down the right flank, but the visitors created another opportunity from distance as Calum Chambers stung the palms of Arrizabalaga from 20 yards out.
Fulham had started to build some momentum heading into the break, but Chelsea almost doubled their lead just before half time when Giroud was denied at the near post after being found by Cesar Azpilicueta.
Ranieri's team went straight onto the offensive after the restart, but it was Chelsea who created the first opening as Pedro saw a right-footed curler comfortably parried away by Rico.
The Blues were starting to get on top but Fulham almost found an equaliser twice in the space of a minute, with Antonio Rudiger nearly diverting a cross into his own net before Alfie Mawson was superbly denied by Arrizabalaga from the resulting corner.
Chambers was the next man to test the Spanish stopper, who had to dive to his right to keep out a well-struck effort, and it forced Maurizio Sarri into a change with Loftus-Cheek being given rare minutes in the top flight.
Alvaro Morata was also introduced from the bench and the substitute should have wrapped the game up soon afterwards, only for a close-range volley to go well over the crossbar after Hazard had been denied by Rico.
Fulham were always in the game while it remained at 1-0, but with eight minutes remaining Chelsea doubled their advantage when Hazard teed up Loftus-Cheek to his right and the England international produced a fine finish to the left of Rico from 15 yards out.
The Cottagers battled on until the end and would have been full value for a consolation goal, but Chelsea held on to register a clean sheet a week on from their capitulation against Spurs.
CHELSEA (4-3-3): Arrizabalaga; Azpilicueta, Rudiger, Luiz, Alonso (Zappacosta 78'); Kante, Jorginho, Kovacic (Loftus-Cheek 67'); Pedro, Giroud (Morata 70'), Hazard
FULHAM (4-2-3-1): Rico; Christie, Odoi, Mawson, Le Marchand; Chambers, Seri; Cairney (Kebano 76'), Johansen (Ayite 46'), Sessegnon (Kamara 46'); Mitrovic