Jurgen Klopp's side had managed to secure a late comeback to beat West Ham United in the Premier League on Monday
The Reds initially trailed the Hammers in a 2-1 scoreline with just 10 minutes into the second half.
Georginio Wijnaldum opened the scoring with an header in the first ten minutes of the first half, converting a whipped Trent Alexander-Arnold cross from the left flank.
But moments after Wijnaldum's opener, Issa Diop headed in just to level the match for the visitors.
Both teams settled in a 1-1 draw until the second interval when Pablo Fornals completed a remarkable turnaround within ten minutes of play.
With 22 minutes remaining to full time, goals from Mohamed Salah (68) and Mane ensured Liverpool kept their unbeaten run alive.
It was the first time Jurgen Klopp's men had been behind in a Premier League match since a 2-1 win against Aston Villa but in the end they had Łukasz Fabiański to thank for their equaliser when the Polish goalkeeper allowed a tame shot from Mohamed Salah to slip through his fingers.
Liverpool have now equalled Manchester City's Premier League record of 18 consecutive league wins after the victory over David Moyes' side on Monday night.