Chelsea remain in fourth place, but they are now just three points ahead of fifth placed Arsenal in the race to qualify for next season's Champions League.
N'Golo Kante scored the lone goal of the match for Chelsea in the 51st minute.
Eden Hazard scored his 100th and 101st Chelsea goals as Maurizio Sarri's men moved back into the Premier League top four by grinding out a 2-1 win at Watford on Boxing Day.
Eden Hazard provided his ninth assist of the season for Pedro Rodriguez to open the scoring and then chalked up his ninth goal of the campaign.
Eden Hazard's present deal runs till June 2020.
Goals from Pedro and Ruben Loftus-Cheek helped Chelsea beat Fulham 2-0 in the Premier League on Sunday.
Eden Hazard has said he is in a quandary about whether to extend his deal or seek a "dream" move to Real Madrid.
Roberto Martinez's men saw their six-match unbeaten run since reaching the World Cup semi-finals brought to an shuddering halt.
Arsenal take on Sporting CP while Chelsea take on Bate Borisov in their Europa League encounters.
Ross Barkley's 96th-minute equaliser helped Chelsea maintain an unbeaten record under Maurizio Sarri.
Jose Mourinho pointed to the precedents for Chelsea being crowned champions in seasons when Eden Hazard is at his best.
Eden Hazard has been instrumental in Chelsea's unbeaten start under Maurizio Sarri.
Hazard, who led Belgium to 3rd place at the 2018 World Cup, feels it's the right time for a fresh challenge with Madrid as his preferred location.
Ross Barkley set up Eden Hazard's 30th-minute opening goal before adding the second as Chelsea beat Southampton on Sunday.
Daniel Sturridge stunned Chelsea with a late goal to rescue a point for Liverpool.
The showdown between Premier League leaders Liverpool and title rivals Chelsea at Stamford Bridge would be the centre of attention.
Eden Hazard's spectacular goal gave Chelsea a 2-1 win over Liverpool at Anfield in the Carabao Cup.
Maurizio Sarri believes Eden Hazard can become the best player in Europe and outstrip even arch poachers Harry Kane and Mohamed Salah.
