A late goal from Divock Origi sealed the points for the home side. The Belgian scored deep into injury time after an error from Jordan Pickford.
The Everton keeper helped keep Van Dijk’s misplaced shot in the game and Origi nodded in from close range.
The Toffees will be bitterly disappointed with the defeat after having played really well for most of the game. They could have got the three points themselves if the likes of Gomes and Mina had taken their chances.
Liverpool’s Sadio Mane missed a couple of great chances and Xherdan Shaqiri was stopped by Jordan Pickford.