Rafael Benitez, who had been appointed in November, remained without a victory as Chelsea manager after his side fell to a 3-1 defeat at the hands of West Ham United.
Juan Mata fired Chelsea in front early on, but Carlton Cole headed West Ham level just after the hour-mark, and Mohamed Diame and Modibo Maiga then struck for the hosts in the 86th and 91st minutes.
The result left Chelsea in third place on 26 points, 10 points behind league leaders Manchester United and contemplating their worst start to a PL campaign in the Roman Abramovich era.
West Ham, on the other hand, moved up to eighth on 22 points.
Hull City claimed their first ever win over Liverpool in a 3-1 victory at the KCOM Stadium.
The hosts went ahead through Jake Livermore before being pegged back by Steven Gerrard’s pinpoint free-kick.
David Meyler put Hull back in front inside the final 20 minutes and Martin Skrtel’s late own goal ended Liverpool’s hopes of a comeback.
The result left Liverpool fourth on 24 points, seven points off league leaders Arsenal, while Hull moved up to 10th on 17 points.