Everton finally rid themselves of their Anfield bogey with a brilliantly drilled performance in which goalkeeper Jordan Pickford and Michael Keane were excellent, while Richarlison led the line tirelessly.
Richarlison put Everton in front after three minutes when he latched on to a superb pass from James Rodriguez to beat Allison.
Liverpool responded and Pickford saved well from Jordan Henderson, who went off injured in the first half, while Everton captain Seamus Coleman should have added to Richarlison’s strike only to head straight at Alisson from six yards.
Sadio Mane wasted two headed chances for Liverpool in the second half while Pickford saved superbly from Salah, leaving Everton to wrap up their first Anfield win in 24 attempts when substitute Gylfi Sigurdsson scored from the spot with seven minutes left after Dominic Calvert-Lewin tangled with Trent Alexander-Arnold.
Everton manager Carlo Ancelotti was all smiles at the final whistle but this was more abject Anfield misery for his Liverpool counterpart Jurgen Klopp, as his team’s flimsy Premier League title defence crumbles.
Everton finally end the hoodoo
This Anfield means more than just three points for Everton. It means the end of a miserable sequence stretching back to 27 September, 1999 when Kevin Campbell gave Walter Smith’s side a 1-0 win.
Since then, Everton and their fans have endured unrelenting gloom when crossing Stanley Park – so it was no surprise this win was greeted with such joy by manager Ancelotti and his team.
This will be a huge psychological lift for Everton, who have now won eight of their past 12 away games and demonstrated here exactly why they are so good on their travels.
Ancelotti’s smart game plan worked to perfection as he achieved the feat that eluded David Moyes in 11 years in charge as well as his successors, Roberto Martinez, Ronaldo Koeman, Sam Allardyce and Marco Silva.
Everton struck early, then defended magnificently while always carrying a threat on the break, although it took heroics from keeper Pickford, the villain when Virgil van Dijk was injured in the derby at Goodison Park last October, in the vital moments to keep listless Liverpool at bay.
Ancelotti beamed as he embraced his players on the Anfield turf after the final whistle – and no-one can begrudge them their deserved celebrations.