Arsene Wenger’s problems at Arsenal deepened as the Gunners are pushed out of the top 4 in the Premier League
Roberto Firmino opened the scoring on nine minutes and Sadio Mane doubled the lead before the break.
Wenger brought on Alexis Sanchez at the break and the striker fed a lovely throughball to Danny Welbeck for 2-1.
But Georginio Wijnaldum killed off the game in injury time as Liverpool recorded only their third win in all competitions in 2017.
Arsenal have now lost 3 of their last 4 league games.
Elsewhere, Manchester United remained sixth with a draw against 10-man Bournemouth.
Champions Leicester City came from behind to beat Hull City 3-1 as Foxes recorded their second straight win since sacking Claudio Ranieri.
Stoke City eased to a 2-nil win over struggling Middlesbrough.
Swansea came from behind to beat Burnley 3-2.
Southampton bounced backed from their EFL Cup final heartbreak to beat Watford 4-3 at Vicarage Road.
Two Golden Boot contenders go head to head on Sunday as Tottenham’s Harry Kane and Everton’s Romelu Lukaku face off at White Hart Lane.
Relegation battlers Sunderland host Manchester City in Sunday’s other game.