The Eagles opened the clash with Wilfried Zaha's impressive early strike and closed proceedings when Michy Batshuayi netted in the 97th-minute.
However, conceding twice to Tomas Soucek and once from a Craig Dawson header meant Palace would take nothing from their work as the Hammers moved up to fourth.
Zaha and Batshuayi's efforts were undoubted highlights from a frustrating evening, as was a spectacular save by Vicente Guaita to deny Michail Antonio.
To watch these key moments in full and for free, simply head over to Palace TV by clicking here or 'Palace TV' within the app.
