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Palmer sent Bernd Leno the wrong way with his spotkick in the dying moments of the first half after Raheem Sterling was brought down by Issa Diop’s trailing foot.
It was Palmer’s ninth league goal since joining the Blues from Manchester City as a last-minute summer signing and quickly establishing himself as Chelsea’s most dangerous player.
Fulham’s best chance for an equaliser fell to Raul Jimenez whose shot forced Djordje Petrovic into a one-handed save in the 73rd minute. Chelsea captain Conor Gallagher smacked the post with a shot from the outside of his boot in the 83rd minute.
One of the biggest cheers came when Ben Chilwell was sent on from the Chelsea bench, marking the England defender’s return from injury and potentially solving the Blue’s left-back problem which centre-half Levi Colwill has struggled to fix.
The win pushed Chelsea up two places in the league table to eighth, above Manchester United and Newcastle United who both have a match in hand over the Blues. Fulham remained 13th, eight points clear of the relegation zone.
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