Central defender Dejan Lovren and Jordan Henderson score in the first half for Liverpool and Diego Costa scored a consolation goal for the home side in the second half.
Henderson's strike was phenomenal. The midfielder scored from a 25 yards strike in the 36th minute to end Chelsea unbeaten streak in the English Premier League 2016/17 season.
Liverpool dominated the proceedings from the beginning of the match. Last week's hero Roberto Firmino missed the game due to a last minute knock, and Daniel Sturridge replaced the Brazilian as the front striker.
The attacking trio of Sadio Mane, Sturridge and Phillipe Coutinho created problems for the Chelsea defence who was missing their talisman John Terry. New recruit David Luiz got his first start of the season.
Lovren scored the first goal taking advantage of Chelsea's sloppy defending. Coutinho curled a cross into the penalty box and Lovren tapped in.
Henderson increased the goal in the 36th minute with a world class strike which was impossible for Thibaut Courtois to save.
As the second half resumed, Chelsea took the command of the game in their hands. Conte's men attacked in numbers.
Diego Costa scored Chelsea's only goal of the match in the 61st minute from Nemanja Matic's assist.