Manchester City have now won only once in 11 games in all competitions.
In another match in the English Premiership, Manchester United finished with nine men in a 0-1 defeat to Everton.
Manchester United beat Bolton Wanderers 2-1 to go three points clear in the premier league.
A round-up of the weekend's action in the major European leagues.
Midfielder Jordan Henderson's fluke second-half goal kept Liverpool firmly in contention.
Ryan Giggs scored both times for Manchester United; Harry Kewell pulled one back for Liverpool.
The four-times European champions went through 3-2 on aggregate after losing 0-1 in the second leg Champions League quarter-final.
Manager Roy Hodgson has hinted that Liverpool are unlikely to mount a Premier League title challenge this season.
Liverpool will start favourites but PSV Eindhoven coach Ronald Koeman will fancy another English scalp when the Dutch club host the first leg of their Champions League quarter-final on Tuesday.
The result leaves Ole Gunnar Solskjaer's United in 10th with nine points, their worst start after seven games for 30 years, and they have won just one of their last six league games.
Arsenal will host Newcastle United in the outstanding League Cup third-round tie after the draw was made on Saturday.
Steven Gerrard was again Liverpool's saviour on Sunday as the inspirational captain secured a 1-1 draw with Everton in the Merseyside rivals' fourth-round FA Cup tie at Anfield. Gerrard struck nine minutes after halftime to cancel Joleon Lescott's first-half header as the game finished with the same score as their Premier League meeting on the same ground last Monday.
Liverpool flirted with what would have been an embarrassing low in their poor start to the season as they were taken to penalties by fourth tier Carlisle United, but came through to reach the League Cup fourth round on Wednesday.
Liverpool's wide range of goalscorers this season is a direct result of their attacking style, according to manager Juergen Klopp.
Leicester City stumbled on their march towards the Premier League title when they drew 2-2 with West Ham United and had goalscorer Jamie Vardy sent off at the King Power Stadium on Sunday.
Mario Balotelli will return to Liverpool's squad for the festive programme but manager Brendan Rodgers was hardly effusive in his praise of the Italy's striker's credentials.
Liverpool are determined to end the trend of selling their best players during the close season in order to build a squad capable of consistently challenging for major honours, manager Juergen Klopp said.
Liverpool captain Steven Gerrard will be sidelined for at least four weeks with the hamstring injury he picked up last weekend, manager Brendan Rodgers said on Thursday.
Arsenal beat Liverpool 4-2 to take a seven-point lead over Chelsea at the top of the league with seven matches remaining.
Here is a look at the clubs most likely to give City a run for their money next season.
Liverpool's half-baked pre-season transfer dealings have come back to bite them with Brendan Rodgers admitting his side have lacked the quality to finish in the Premier League's top four.
Arsenal also suffered a shock defeat when they went down 2-1 at Stoke City and Hull City came from 1-4 down to push Manchester United all the way before losing 4-3 at Old Trafford, in the English Premier League.
Holders Barcelona suffered a stunning 2-1 home defeat by Russia's Rubin Kazan while Liverpool lost by the same score to Olympique Lyon at Anfield on a night of high drama and late goals in the Champions League on Tuesday.
Arsenal beat north London rivals Tottenham Hotspur 3-1 to surge top of the English Premier League.
City have 89 points, one more than rivals Liverpool, with both teams having three games to play -- and none of them against top six opponents.
Two defeats and a draw from their first three matches in Group A left Liverpool in the mire and needing a Houdini-like escape act to stay alive
Fans are openly speculating that owner Roman Abramovich, a man who places notoriously high demands on his managers, could call time on Jose Mourinho's second spell at Stamford Bridge if Liverpool can inflict another defeat on the champions.
Aston Villa blew a chance to go eight points clear of Arsenal in the race for England's fourth Champions League berth Sunday after conceding two late goals against relegation-threatened Stoke City. The 2-2 draw, with Stoke cancelling out their hosts' 2-0 lead in the final three minutes, left fourth-placed Villa six points ahead of Arsenal and three adrift of second-placed Chelsea and Liverpool in the Premier League.
Images from the English Premier League matches played across England on Sunday.
Manager Arsene Wenger has silenced his critics with Arsenal's rip-roaring start to the season, club great Dennis Bergkamp said on Friday.
Liverpool manager Juergen Klopp called for his players to "stay calm" and does not expect to expect wholesale changes against Burton Albion on Tuesday as they seek to quickly bounce back from their 2-0 defeat at Burnley.
Photos from the English Premier League matches played on Sunday
Former Arsenal, Spain midfielder Fabregas hangs up his boots, to coach Italian club.
After a six-match unbeaten start to his reign as Liverpool manager Juergen Klopp came down to earth with a bump as his side lost 2-1 to Crystal Palace in the Premier League on Sunday.
A stunning strike from Jordan Henderson helped Liverpool secure a comfortable 2-1 win at Chelsea on Friday that ended the London club's unbeaten start to the season and underlined the growing potential of Juergen Klopp's side.
Liverpool kept their push for a top-four finish in the Premier League on course as Emre Can thundered home a second-half winner to complete a hard-earned 2-1 comeback win over Burnley at a relieved Anfield on Sunday.
Favourites Barcelona will meet Benfica in the quarter-finals of the UEFA Champions League.
Mauricio Pochettino has left his job as Chelsea manager by mutual consent, the Premier League side announced on Tuesday.
Liverpool's Mohamed Salah ended his Premier League goal drought in style by scoring twice as the champions raided the capital again to crush West Ham United 3-1 on Sunday.
