West Ham had endured a miserable week with Dimitri Payet having refused to play for the club, but Carroll's wondrous 79th-minute effort, a mid-air volley from Michail Antonio's cross, brought the smiles back to the Hammers' faithful.
His goal came 11 minutes after Sofiane Feghouli had scored his first Premier League goal from close range and Manuel Lanzini went on to seal Palace's misery with an outstanding run and finish four minutes from fulltime.
It left Palace only to reflect miserably on how ex-Hammer James Tomkins had missed from point-blank range with the best chance of the first half and left Allardyce winless after his first five matches at the helm at Selhurst Park.
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(Reporting by Ian Chadband; Editing by Toby Davis)
