Zaha struck early on to give Palace the lead, while Gallagher sealed the victory in the final few minutes to send the travelling fans into ecstasy and the Eagles home with three points.
The two goals bookended an action-packed clash that saw drama at both ends, as Aymreic Laporte was sent off late in the first-half, and Gabriel Jesus had a goal ruled out by VAR.
Check out all the highlights below or on Palace TV!
