The Seagulls were playing at Selhurst Park on Thursday night and played out a largely uneventful first half until a blunder from the Dutch goalkeeper led to the goal.
Roberto De Zerbi's side are one of the best in the Premier League when it comes to playing out from the back, but the 21-year-old goalkeeper endured a moment to forget as his pass from the back was intercepted by Michael Olise.
The ball fell to Will Hughes who slotted it back to the French star on the right-hand side of the penalty area before floating a beautiful ball into the back post.
It was there that Ayew ghosted in and headed home to give the home crowd something to cheer about.
While Verbruggen's error ultimately led to Palace's goal, credit must also go to Chris Richards for putting the Seagulls' summer signing under the sort of pressure that led to such a mistake.
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Brighton appealed for a penalty in the second half when Jake Hinselwood went down in the area, however the young midfielder appeared to trip himself, meaning that no foul occurred.
But Danny Welbeck was able to spare their blushes with a wonderful looping header to make it 1-1 late in the game.
Palace are on a torrid run of form having failed to win in their last six matches in all competitions.
However, their last result was a spirited 2-2 draw against Manchester City and the hope will be that a draw at Selhurst Park will be a step towards getting themselves back on track.
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As for Brighton, that draw means that they miss the chance to leapfrog Manchester United, leaving them in eighth position in the Premier League.