Southampton held Tottenham Hotspur to a 1-1 draw while West Ham bowed out of the FA Cup after being beaten 1-0 by West Bromwich Albion.
Ole Gunnar Solskjaer's side suffered a third defeat in their last four Premier League games to put the Manchester United boss' job security back under the microscope.
A slump in form from Frank Lampard's men has left the door open for Manchester United, Tottenham and Arsenal to secure a much-needed return to Champions League.
Fernandinho's late own goal forced Manchester City to settle for a 2-2 draw against Crystal Palace, while Tottenham were held to a goalless draw by Watford.
Robbie Keane's son Hudson made off with the football even as the teams were lining up ahead of the Middlesbrough vsTottenham Hotspur match recently.
Tottenham edged into the FA Cup fourth round as Giovani Lo Celso bagged a rare goal in their 2-1 win over Middlesbrough.
Jose Mourinho was questioned about Harry Kane and his answer suggested there could be some doubt over the 26-year-old's participation at Euro 2020.
Barcelona's open hankering after Xavi has left a bitter taste, particularly with those who believe Ernesto Valverde, who always speaks with sense and integrity, deserves better.
Liverpool have earned 61 points from a possible 63 in 21 games to streak 16 points clear at the top and with a game in hand over second-placed Leicester.
Liverpool haven't lost a game in the league this season and are on top of the points table with 58 points from 20 games, while Tottenham Hotspur are sixth with 30 points from 21 matches.
Harry Kane has scored 27 goals in 31 appearances for club and country this season and his loss is a huge setback for Tottenham.
Antonio Rudiger had complained that he was subjected to monkey chants in Chelsea's 2-0 win at Tottenham Hotspur on December 22.
FA Cup Draw: Liverpool face a trip to either Bristol City of the Championship or Shrewsbury Town of League One as holders Manchester City take on Fulham.
Teenager Curtis Jones sealed a 1-0 win for Liverpool against Everton while Chelsea thrashed Nottingham Forest 2-0 in the FA Cup.
Jose Mourinho said that Tottenham need to be intelligent and make the right decisions in the transfer market for the "development of a cycle".
Harry Kane limped off during Tottenham's 0-1 defeat to Southampton on New Year's Day and the club are set to find out the extent of the problem before the weekend.
Chelsea boss Frank Lampard is expected to make a big splash after being unable to sign players in the summer window due to the club's transfer ban.
There was little response from Jose Mourinho's men as they slipped six points behind fourth-placed Chelsea.