Eberechi Eze converted from Tyrick Mitchell's cut-back to finish off a flowing Palace move early on and the visitors were deservedly in front at the break.
Mohammed Salah scored his 200th Liverpool goal before Harvey Elliott snatched a 2-1 victory at 10-player Crystal Palace, sending the Reds top of the Premier League.
But Palace, now four matches unbeaten in the league, showed fighting spirit to come back with minutes left to play, after being the better team in the first half.
Palace had chances to extend their lead, Jean-Philippe Mateta having one effort cleared off the line by Andy Robertson and another saved superbly by the returning Alisson but they did not need a second.
Chelsea equalled a club record as they beat Crystal Palace to secure their 11th successive Premier League win and move nine points clear at the top of the table.
Julian Speroni kept Palace in the game with a series of fine saves before Darmian doubled the lead by lashing home from 20 yards. Arsenal, who have a game in hand, entertain West Brom on Thursday.
Goals from Oscar, Willian and Costa secured a 3-0 win over Crystal Palace. It will be Chelsea's first win under Hiddink and their first of the new year.
Dr Sid, Tiwa Savage and newbies Di’Ja, Reekado Banks, Korede Bello gave a stunning performance of The Mavin's hit single “Dorobucci” at the “Road To MAMA” concert which held at Federal Palace Hotel in Lagos on Friday, May, 30, 2014. Watch!
Crystal Palace hit four goals in the first 31 minutes as they thrashed sorry West Ham at Selhurst Park. Michael Olise opened the scoring when he rose highest to convert Joachim Andersen's lofted ball into the box.