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Strikes from Mohamed Salah, Andy Robertson, Cody Gakpo and Harvey Elliott earned the victory for Klopp's men, who had won one of their previous five league games and seen their title challenge crumble.
Haaland made a quick impact when he entered the game as a substitute in his first action since missing two matches with a muscle injury.
Foden struck twice as Manchester City stepped up their bid for a fourth Premier League crown in a row with a ruthless 4-0 victory at Brighton & Hove Albion.
It was the sixth time Arsenal have scored five or more in a Premier League game this season without conceding and in such a tight race they now have a huge goal difference advantage which could prove crucial to the outcome.
Arsenal's defeat, their first in 12 league games, sees them remain second, two points behind City and level on points with third-placed Liverpool with six games left to play.
Federico Valverde salvaged a draw for Real late on after City had taken a 3-2 lead with sumptuous strikes from Phil Foden and Josko Gvardiol following a Ruben Dias own goal and Rodrygo strike that gave the hosts a half-time lead in Spain's capital.
Manchester United fanned the embers of their top-four hopes with a 2-0 win against visiting Everton.
Paris St Germain's Kylian Mbappe scored twice to lead them into the Champions League quarterfinals.
Van Dijk rose high above his marker to head a corner back across goal and into the far corner in the 118th minute.
The German joined Liverpool in October, 2015, and has won the Champions League, Premier League, Club World Cup, FA Cup, League Cup and Super Cup, as well as the Community Shield during his time in charge.