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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.
A point moves Tottenham level with north London rivals Arsenal, just outside the top four only on goal diference.
The 37-year-old Lloris, whose contract with Spurs was due to expire in June, has signed a one-year deal with an option to extend for 2025 and 2026 after an 11-year stay in London.
Pep Guardiola's newly-crowned FIFA World Club champions had lost ground in the title race after a run of one win in six league games.