Alan Pardew???s side made the perfect start as Jedinak latched onto Scott Dann???s flick-on and bundled the ball into the back of the net in the third minute.
They doubled their advantage in the 16th minute when Chung-yong Lee pounced on a mistake by goalkeeper Ronwen Williams before firing a low finish into the bottom corner.
Palace made it three 12 minutes later as Mutch produced a brilliant solo run, beating two players and chipping the goalkeeper from close range.
Moments later the visitors were on the scoresheet again as Jason Puncheon???s shot deflected into the path of Campbell, who produced a cool finish to send his side into the break four goals to the good.
New signing Bamford, who completed his loan move to Selhurst Park from Chelsea on Tuesday, entered the fray at the break but neither side threatened amidst a wave of substitutions.
Pardew also sent on Yohan Cabaye midway through the second half as Palace tried to add to their four first-half goals and he was immediately in the action, sending over inch-perfect through ball for Bamford who was then denied by Williams.
Cabaye’s influence grew as the game went on and he created an opening for himself in the 67th minute, skipping away from a challenge but he could not get his shot away.
Palace continued to press forward and with just 10 minutes remaining Cabaye danced his way past two challenges before slipping the ball to Sullay Kaikai but the pass was intercepted just before the 19-year-old could get a shot away.
Supersport had one final chance to pull a goal back but in the dying stages??Thuso Phala missed an open goal to keep the score at 4-0.