Everton counterattacked and striker Romelu Lukaku, pursuing a goal in an eighth straight match, was denied by a brilliant slide-tackle from Chancel Mbemba in the penalty area. From the resulting corner, Rob Elliott cleared with a weak punch, and Cleverley managed to loop a header over the goalkeeper and in.
Everton goalkeeper Tim Howard earlier made an excellent save from a point-blank Georginio Wijnaldum header.
Newcastle drops to 18th and into the relegation zone, and Everton rises to ninth.
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