Luis Suarez set up one goal and scored another to put the visitors 2-0 up inside 20 minutes, celebrating his role in the opener with a gleeful dive right in front of the Everton dug-out.
It was aimed as a rebuke to Moyes, who had criticised the Uruguayan for diving in the build-up to the game, but Everton reacted quickly and drew level before half-time through goals from Leon Osman and Steven Naismith.
Suarez thought he’d had the final say after poking the ball home in the fourth minute of injury time, but the goal was controversially ruled out despite the Liverpool striker being onside.
The result took Everton into the top four, bumping Arsenal down to fifth place, while Brendan Rodgers’ Liverpool lie six points below their city rivals in 11th.
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