But Claudio Ranieri's side, who qualified for the last 16 of the Champions League in midweek, refused to buckle and averted what would have been a third consecutive Premier League defeat.
Liverpool 2-0 Sunderland
Substitute Divock Origi and James Milner both scored as Liverpool beat Sunderland 2-0 at Anfield to return provisionally to the Premier League summit on Saturday.
Liverpool dominated possession without finding a way past Sunderland's stubborn defence, spurning a host of chances until Origi, on in the first half for the injured Philippe Coutinho, curled in his first league goal of the season in the 75th minute.
Milner wrapped up the points from the penalty spot in the 91st minute, sending Sunderland goalkeeper Jordan Pickford the wrong way after Sadio Mane was brought down in the box by Didier Ndong.
Liverpool rose to the top of the Premier League table with 30 points, two ahead of third place Chelsea, who can return to the summit with victory over Tottenham Hotspur later on Saturday. The defeat sent Sunderland back to the bottom of the standings.
Swansea 5-4 Crystal Palace
Fernando Llorente's two injury-time goals saw Swansea come from behind to snatch a thrilling 5-4 win over Crystal Palace in an amazing see-saw game at the Liberty Stadium.
For Swansea the win snapped an 11-game winless streak and for Palace it handed them their sixth straight defeat.
Wilfried Zaha opened the scoring for Palace but Bob Bradley's Swans looked set for their first win since the opening day of the season as a Gylfi Sigurdsson free-kick and a brace from Leroy Fer put them 3-1 midway through the second half.
Unbowed, Alan Pardew's Palace came roaring back, James Tomkins forcing home a corner and Jack Cork deflecting the ball into his own net before Christian Benteke put the visitors 4-3 up with just six minutes left.
But Llorente netted twice in the 91st and 93rd minutes to put the home side back on top, and they hung on grimly through seven minutes of injury time for the three precious points that take them off the bottom of the table.
- AAP