Coach Arne Slot established early control when Ryan Gravenberch’s clever lofted finish from Mohamed Salah’s pass put Liverpool ahead after 10 minutes.
Gravenberch turned provider just before the half-hour mark when he played on Hugo Ekitike to beat Everton keeper Jordan Pickford with a low shot.
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Liverpool illustrated the strength of their squad by leaving Florian Wirtz and Alexander Isak, two summer signings worth a combined total of £241m, on the bench until the second half.
Everton improved as the game went on, pulling a goal back after 58 minutes when Jack Grealish’s cross found Iliman Ndiaye at the far post and he set up Idrissa Gueye for a powerful rising drive that left Liverpool keeper Alisson helpless.
Liverpool remain number one on the EPL’s table, with 15 points, while Arsenal follows with 9points, after losing to the Red last weekend.
