The Reds came from behind to record a convincing victory over the Premier League champions.
Klopp replaced Brendan Rodgers as Liverpool manager before the international break and has yet to lose as Reds boss.
Emre Can started in midfield and helped the Reds control possession for most of the game completing the highest number of passes in midfield (74) at an 84 percent.
Can worked hard on the defensive end and contributed in the final third with two key passes – joint highest in the team.
The win took Liverpool into 7th place on 17 points meanwhile Chelsea languish in 15th place on 11 points.
Chelsea 1 – 3 Liverpool
Stadium: Stamford Bridge
Chelsea lineup: Begovic; Zouma, Cahill, Terry (c), Azpilicueta; Mikel, Ramires; Willian, Oscar, Hazard; Diego Costa.
Manager: Jose Mourinho
Liverpool lineup: Mignolet, Clyne, Skrtel, Sakho, Moreno, Lucas, Can, Milner, Lallana, Coutinho, Firmino
Manager: Jurgen Klop