Pedro opened the scoring for the home side after just five minutes, with a first-time effort from the edge of the box after a short corner.
Summer signing Zappacosta doubled Chelsea's lead on the half hour mark with a solo effort as he raced down the right flank, beat a defender and saw his cross-cum-shot fly in.
Chelsea had to settle for a 2-0 lead at the break, but then ran riot with four further goals in the second period.
Cesar Azpilicueta headed home a Cesc Fabregas delivery, before Bakayoko made it four with a deflected effort from close range.
Michy Batshuayi, who was handed a rare start, hit a brace in the final 15 minutes to complete the rout, with a shot from outside the area and then a scrambled finish from Zappacosta's cross.