London
Ghanaian midfielder Schlupp struck against the run of play in the 41st minute with a fierce shot from a tight angle and Zaha sealed the win in the closing stages when he rounded Fulham goalkeeper Fabri and slotted the ball into an empty net.
Palace goalkeeper Wayne Hennessey made a string of good saves in the opening half, twice denying Fulham striker Aleksandar Mitrovic after he had also kept out a long-range shot from right back Cyrus Christie.
The visitors had the upper hand after the break and although Zaha saw his close-range volley kept out by Fabri on the hour, the livewire Ivorian forward made no mistake in the 79th minute after a defence-splitting pass by Aaron-Wan Bissaka.
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