Mark Noble fired the visitors into a first-half lead from the penalty spot. Palace would have equalized earlier but midfielder James McArthur tried to lift the ball over 'keeper Lukasz Fabianski, only to clip it wide from four yards out.
Instead it was Zaha, sent off at Southampton last week after sarcastically clapping the referee, who milked the applause with his late leveler. West Ham took a 27th-minute lead when Declan Rice lofted the ball into the box. Palace goalkeeper Vicente Guaita came out and clattered into Michail Antonio. The reliable Noble stepped up to take the spot kick, sending Guaita the wrong way for his first goal of the season.
The equalizer arrived after 76 minutes when Zaha ran at the West Ham defense, collected a return ball from McArthur and saw his angled drive loop off the boot of Issa Diop and over Fabianski. Midtable West Ham has six more points than Palace.
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