Jurgen Klopp’s side beat Arsenal on their own patch on the opening day of the campaign.
And they followed that up with a win over Chelsea tonight on their second visit to the capital this term.
Goals from Dejan Lovren and Jordan Henderson did the business, although Diego Costa pulled one back from the hosts.
Liverpool were cruising at the break.
Centre-back Lovren put Jurgen Klopp’s side in front with a classy finish from a Philippe Coutinho cross.
The Brazilian whipped in a devilish delivery and the unmarked Croat stroked the ball past a helpless Thibaut Courtois.
Belgian ace Courtois could do nothing about Liverpool’s second either as Henderson put the Reds in control.
The Kop skipper found time and space outside the area and curled a terrific effort into the top corner of Courtois’ net.
Chelsea fired back in the second and dragged themselves into the game with Costa’s strike on the hour mark.
The big frontman did the business from close range after a Nemanja Matic.
Antonio Conte’s side could find a second though, and it was Liverpool who went closest to the next goal when Courtois clawed away a goal-bound header from Divock Origi.
FULL REPORT TO FOLLOW