Ayew could have opened his account as early as the third minute when spotted by Abraham in the box, but he headed wide from the game's first chance.
The Swans stepped up a gear midway through the first half, though, and they were ahead before the break thanks to Abraham's volleyed finish to get the beating of Hennessey, who had earlier denied the striker with a big stop.
Palace, without a goal in seven of their last eight league outings - all of which have ended in defeat - looked to drag themselves back on level terms through a Martin Kelly header that Lukasz Fabianski was well placed to keep out.
Ayew netted a killer second 48 minutes in to dent the Eagles' hopes, however, poking the ball past Hennessey after Kyle Naughton stole it from Kelly in midfield to play his teammate through on goal.
Andros Townsend failed to convert when in a promising position 10 minutes from time, with the blunt hosts unable to find a way through as their slow start to the season continues.