Liverpool took the lead against West Ham United but then had to come from behind in another game of thrills and spills for Juergen Klopp's unpredictable side who where held to a 2-2 home draw in the Premier League on Sunday.
Liverpool, six points adrift of leaders Chelsea, managed one goal in four games with West Ham last season but took just five minutes to score at Anfield when Adam Lallana turned cleverly to meet Sadio Mane's cross and shoot low into the net.
However, West Ham got back on level terms when Frenchman Dimitri Payet fired a 20-metre free kick past goalkeeper Loris Karius who, as at Bournemouth in last week's 4-3 defeat, should have done better after getting a hand to the ball.
Another Liverpool mistake led to West Ham's second goal when Joel Matip, supposed to be the calming influence in defence, failed to clear a ball that looped over his head and fell for Michail Antonio, who slotted past the stranded Karius.
Third-placed Liverpool, though, did not have a trademark on mistakes and three minutes into the second half West Ham keeper Darren Randolph flapped at another Mane cross, leaving Divock Origi a simple job to bag his fourth goal in as many games.
Anfield expected another goal to come although, given Liverpool's current mood, no one could be sure at which end. Jordan Henderson and Nathaniel Clyne went close as the hosts tried to capitalise on their almost total control of possession.
Time and again intricate passes took Liverpool into the visitors' area before each move broke down as West Ham threw enough bodies in the way to hang on for the point that lifts them out of the relegation zone.
(Reporting by Neil Robinson; Editing by Tony Jimenez and Ken Ferris)