Olivier Giroud expertly headed in Victor Moses' cross in the primary half after Liverpool had ruled ownership and neglected to underwrite.
Eden Hazard approached after the break before Marcos Alonso's effective volley flew hazardously past the post. Chelsea stay in fifth yet move inside three purposes of third-set Liverpool.
With two amusements staying to Liverpool's one, Chelsea can put weight on the Champions League finalists with triumph against Huddersfield on Wednesday, albeit given their prevalent objective distinction the Reds would more likely than not guarantee a best four complete with triumph at home to Brighton on the last day.
The guests had over 66% ownership in the principal half and made a lot of chances - the best tumbling to Sadio Mane, who was denied twice by Thibaut Courtois - however it was Chelsea who came nearest. Tiemoue Bakayoko's header skiped inches wide only minutes previously Giroud jumped high to gesture home Moses' cross.
What's more, Cesc Fabregas' brilliant keep running in behind the barrier made an opening which he couldn't change over from a tight edge.
Chelsea had the best odds of the second half as well. Danger nearly moved his way through before Antonio Rudiger's header was precluded for offside.
