The Eagles came into this tie winless in their last two top-flight outings, losing 4-0 at Tottenham Hotspur before playing out a 1-1 draw at home to Wolverhampton Wanderers last time out.
There was none of that struggle this time, with penalty specialist, Luka Milivojevic, giving Roy Hogdson’s side the lead from the spot in the 21st minute, after Ibrahim Amadou tripped James McArthur in the 18-yard box.
The South London club sealed the deal in injury time with Ivory Coast’s Wilfried Zaha assisting Andros Townsend for the second goal.
Ayew got booked for a challenge on Ben Godfrey in the 59th minute and was replaced by Max Meyer 30 minutes later. His Ghanaian teammate Jeffery Schlupp also received a yellow card just before the second goal was scored.
A London derby at West Ham United comes up next for Palace on October 5.