Before the late drama, Dominic Calvert-Lewin headed the equaliser after Mohamed Salah had put the visitors 2-1 ahead with a sweet strike.
Liverpool’s Sadio Mane had opened the scoring early on before the Reds lost defender Virgil van Dijk after a reckless challenge by Everton goalkeeper Jordan Pickford.
Michael Keane then headed the hosts level from James Rodriguez’s corner.
The in-form Calvert-Lewin levelled once again with nine minutes to play before Richarlison was sent off for a dangerous tackle on Thiago at Goodison Park.
The result means Everton maintain their three-point lead at the top of the Premier League.
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