Italy right-back Zappacosta, on his first Blues start, ran 50 yards down the right wing, before sending over a cross that flew past Ibrahim Sehic.
Cesar Azpilicueta headed home a third after the break from Cesc Fabregas' cross.
Willian hit the crossbar, and substitute Tiemoue Bakayoko scored his first Blues goal with a deflected shot from close range.
Batshuayi then scored twice in the final 15 minutes - firing in from outside the box after being picked out in space by Bakayoko and then scrambling home Zappacosta's cross.
Goals: Chelsea 6 (Pedro 5’, Zappacosta 30’, Azpilicueta 55’, Bakayoko 71’, Batshuayi 76’, 82’)
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