After dominating a goalless first half, the Eagles finally edged ahead on 59 minutes when Luka Milivojevic netted his third penalty of the campaign, but with 13 minutes to go, substitute Ayew’s blast from 25 yards levelled things up.
Roy Hodgson’s team couldn’t find a way to get back ahead in the final stages, but they claimed their 18th point of season at the campaign’s halfway point to continue their recent recovery.
Just as they had at Leicester City a week earlier, the visitors started the brighter and minutes into the contest Scott Dann drove a header from a Yohan Cabaye corner at Lukasz Fabianski which the keeper stopped on his goalline, and then on 10 minutes Ruben Loftus-Cheek won possession on halfway and linked up with Wilfried Zaha to create a shooting chance for Andros Townsend who obliged, and forced Fabianski into a fine full-stretch save to tip the ball away from his top corner.
However, moments later the Swans and their fans were screaming for a penalty when Jeffrey Schlupp challenged Luciano Narsingh from behind the area but fortunately for the Eagles Craig Pawson waved play on, but Palace continued to look dangerous on the counter-attack and nearly broke the deadlock when Loftus-Cheek bent a shot just past the far post after the hosts once again coughed up possession in a dangerous area.
All the chances fell to Hodgson’s team in the first half with Julian Speroni untroubled throughout the opening 45, and five minutes before its conclusion some more superb direct running by Townsend saw him reach the edge of the area and pick out the on-rushing Zaha but his stabbed effort went wide.
The goalmouth action dried up after the break with both teams failing to look threatening in the final third, but on 58 minutes that all changed. Loftus-Cheek tricked his way into box and drew a foul from Swans skipper Federico Fernandez, and back on spot-taking duties, Milivojevic waited for Fabianski to commit and smashed the ball straight down the middle to hand Hodgson’s team the lead they merited.
Finding themselves a goal down, the hosts knew they had to be more adventurous and on the hour mark Tammy Abraham finally produced a shot of note as he forced himself into the box and let fly but drilled high and wide, and then five minutes later the striker had a second opportunity when Narsingh sped down the right and found the on-loan Chelsea man, and after a neat chest-down handed him a sight of goal, Speroni came out and blocked the attempt with his leg.
A second for Palace would have ended the contest, and Zaha nearly produced it when a fantastic run by the industrious Townsend allowed him to play in his striker partner who could only shoot tamely at Fabianski, but such were the fine margins that their one-goal lead was a fragile one and Speroni was forced to scramble across his goalmouth to edge a deflected Nathan Dyer cross away from danger.
But with 14 minutes to go, Leon Britton’s side did find a leveller in fine style. Tom Carroll laid the ball off to substitute Ayew 30 yards from goal, who dummied past Milivojevic to create some space, and he made the most of that to thump a stinger through a crowd of players and past Speroni to hand the hosts a lifeline.
He nearly added a second from range a couple of minutes later but saw his bouncing effort fizz wide of Speroni’s far upright, but despite plenty of late pressure from the Welsh side, Palace held on to return to south London with another useful point.
Swansea: Fabianski, Naughton (Rangel 80), Fernandez, Mawson, Olsson, Clucas, Mesa (Fulton 89), Carroll, Narsingh (Ayew 66), Dyer, Abraham. Subs not used: Nordfeldt, Van der Hoorn, Sanchez, McBurnie.
Palace: Speroni, Kelly, Tomkins, Dann, Schlupp, McArthur, Milivojevic, Cabaye (Sako 76), Loftus-Cheek, Townsend (Van Aanholt 85), Zaha. Subs not used: Hennessey, Souare, Fosu-Mensah, Riedewald, Puncheon.