The hosts were on top for the early parts of the game and made their advantage count through Pablo Fornals just before half-time.
The Eagles were trailing going into the break, but responded brilliantly in the second-half.
Loanee Conor Gallagher levelled it for the Eagles just before the hour mark, though the Hammers took the lead once more through Michail Antonio.
Palace showed their resilience to respond immediately through Gallagher. The midfielder levelled it for the Eagles in the 70th minute with an excellent bit.
Marc Guéhi nearly secured all three points for the Eagles in stoppage time, though his header went narrowly over the bar.
Check out all the highlights below!