Jurgen Klopp’s side picked up their first victory of 2016 with a dominant display — just three days after their Wembley heartbreak against Manchester City.
Adam Lallana, who missed Liverpool’s final spot-kick in the Wembley defeat, got the ball rolling in the 34rd minute with a 20-yard strike that keeper Joe Hart seemed to misjudge.
Former City midfielder James Milner doubled their lead six minutes later before Roberto Firmino added a third in the second half.
It’s another serious dent to City’s title hopes as they missed the chance to cut the gap on leaders Leicester City, who they trail by 10 points although they do have a game in hand. But they could have put themselves firmly back in the race with fellow rivals Tottenham Hotspur and Arsenal surprisingly slipping up.
As it is, they will now be looking nervously over their shoulder with neighbours Manchester United moving level on points in the final Champions League spot while West Ham are just a point behind.
But it was hardly surprising given City have only won once in their last 28 attempts at Anfield — now losing on their last three trips.
More importantly for this season’s hopes, it was their third successive Premier League defeat in their worst run since November 2008.
Liverpool made five changes from the side beaten at Wembley, with striker Daniel Sturridge missing from the 18-man squad while Phillipe Coutinho, who had scored five in his last six appearances against City, was left on the bench. Lucas Leiva also dropped out altogether after injuring himself missing a penalty in the shootout defeat.
For City, penalty hero Willy Caballero returned to the bench with first-choice keeper Hart back in the side. Yaya Toure also dropped out after his winning kick secured the first silverware of the season.
Raheem Sterling kept his place in the side on his first return to Anfield since his controversial £44m switch. Liverpool fans booed him throughout the Cup final triumph and he unsurprisingly received the same treatment back in Merseyside.
They took particular pleasure when an ambitious 25-yard strike drifted high into the Kop and even more joy when he was substituted during half time.
Sterling’s wasteful shot was a rare sight of goal for City who looked the more affected by Sunday exertions. They made a sluggish start as Liverpool used their high pressing game, which had been so effective when they thrashed the Blues 4-1 at the Etihad Stadium in November.
But the home side struggled to create chances, with Roberto Firmino drilling a low shot into the midriff of Hart their only chance of the opening half hour.
That changed in the 34th minute when Lallana fire in a low shot that surprised everyone by nestling in the bottom corner. Even Liverpool boss Klopp looked surprised, along with the home fans, before they both finally celebrated the opener.
They doubled their lead six minutes later when Milner latched onto Firmino’s pass to race into the box and finish comfortably under Hart.
City threw on strikers Wilfried Bony and Kelechi Iheanacho as they tried to chase the game but they were carved open again when Lallana found plenty of space in midfield to tee up Firmino, who finished easily from 12 yards.
Milner almost grabbed a second with a 20-yard strike that Hart tipped over the bar while Jordan Henderson fired a free-kick just off target.
Mignolet 6, Clyne 6, Toure 7, Lovren 7, Flanagan 6, Henderson 6, Can 7, Milner 7, Lallana 7, Firmino 8 (Allen 75, 5, Origi 6 (Benteke, 5).
Hart 5, Zabaleta 6, Clichy 6 (Kolarov 75), 5, Kompany 6, Otamendi 5, Fernando 6, Fernandinho 6 (Iheanacho 6, 55), Navas 6, Silva 6, Sterling 5 (Bony 46, 6), Aguero 5.