Portsmouth ran out 6-1 winners as they overwhelmed Leeds United at Fratton Park.
The visitors had conceded 10 goals in their previous three matches, and fell behind to Dejan Stefanovic's strike on 16 minutes.
Alan Smith equalised three minutes later, but Gary O'Neil soon had Portsmouth back in front, just before half-time.
Second-half goals from Hayden Foxe, another from O'Neil, Patrik Berger and Yakubu completed a comprehensive win.
The result left Portsmouth in 11th on 15 points, while Leeds were at the bottom with eight points.
Diego Costa netted the winner as Chelsea recovered from a goal down to maintain their unbeaten start to the 2014/15 campaign.
This became Liverpool's fifth league defeat of the season, despite them going in front through Emre Can's ninth-minute goal.
Gary Cahill equalised for Jose Mourinho's men, before Costa scored his 10th league goal of the season.
Chelsea stayed top on 29 points, with nine wins and two draws from 11 matches. The defeat left Liverpool 11th on 14 points.