Swansea took the lead through Abraham, who fought off Martin Kelly to score with the Welsh side’s first shot on target of the season.
Ayew then doubled Swansea's tally just after half-time, one-on-one with the goalkeeper before finishing with a bit of luck.
Tactical battle consumed the first half
Swansea started the game in a similar 3-5-2 shape that lost 4-0 to Manchester United, but Mike van der Hoorn makes his first start since Boxing Day, replacing the injured Kyle Bartley and new signing Sam Clucas made his debut for the club.
The first chance of the game fell to Ayew, latching onto the end of Abraham’s cross but his header flew just wide of the goal.
Palace then had a couple of chances, Patrick van Aanholt cut the ball back to an empty penalty area before James McArthur took the ball off of Christian Benteke’s head just as the Belgian looked to have a free header.
Swansea struggled to build attacks despite dominating early possession. The players didn’t appear to trust van der Hoorn in possession, forcing wing-back Kyle Naughton to drop deep to receive the ball. This meant that Swansea lacked width especially on the right-flank.
Palace would press when Alfie Mawson was on the ball, and ease off when Federico Fernandez or van der Hoorn were in possession. A smart move by Frank de Boer, in a game he described as a “must-win.”
Abraham almost capitalised on Timothy Fosu-Mensah’s error, stabbing an effort towards goal from a few yards out but Wayne Hennessey made sure to send an already off target effort wide.
Mawson then met the resulting corner with a free header, but sent his shot wide as Swansea were still in search of their first shot on target of the Premier League season.
Abraham then scored with Swansea’s first Premier League shot on target of the season, getting the better of Kelly who was holding him back, but got enough on the shot to beat Hennessey.
It was not the cleanest strike Abraham will ever hit, but it is a goal that will give the 19-year-old confidence in a season where Swansea will rely on him.
Second half will satisfy Swansea
Palace came out of half-time looking bright, forcing Lukasz Fabianski into a good save from Kelly inside a minute of kick-off.
However, Swansea stuck again through Ayew after Kyle Naughton intercepted possession and set the striker through on goal for him to beat Hennessey.
The goal is just Ayew’s second for Swansea since signing for the club in January.
While de Boer still needs time to implement his tactics at Palace, they looked very passive in possession and three losses going into the international break will not be pleasant reading for the Dutchman.
However there is still time left in the transfer window for players to come in, and Yohan Cabaye, Ruben Loftus-Cheek and Wilfried Zaha getting fit again will be huge for the Eagles.
Palace did get back into the game though, and Andros Townsend found some good positions but they were not able to create any clear-cut chances.
Townsend himself had a late chance, after the ball fell to him following a cluster of headers inside the area, the winger tried to place the ball in the corner but didn’t get enough curve on the ball and it skimmed wide.
It was a very professional performance by Swansea, something that has become customary under Paul Clement. They defended very well and took their chances when they got them, he will be very pleased.
The result leaves Palace on zero points from three games, while Swansea sit on four points.
However, the last time Palace lost their first three opening games they ended up getting promoted under Ian Holloway, so a disastrous start may not be the end of the world for the Eagles.