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Everton took all three points at Goodison Park with Gylfi Sigurdsson’s penalty after 22 minutes proving the difference after Edouard Mendy had bundled over Dominic Calvert-Lewin.
The defeat to Everton ended Chelsea’s 17-game unbeaten run across all competitions.
Speaking after Everton’s victory over Chelsea on Saturday night, Everton boss Carlo Ancelotti said: “We needed this performance. We needed these points.
“After a difficult period, we needed to move on and tonight the performance was really good.
“Defensively we didn’t concede opportunities, just a couple of set pieces and long shots. We were well organised.”