Palace's Julian Speroni was the busier of the two goalkeepers during the first half, but he proved to be a match to two efforts from England youth international Nathan Delfouneso in first the eighth and then the 42nd minute.
© PA Photos
Despite their domination, the half ended on a bad note for the hosts when Scottish midfielder Barry Ferguson was handed his marching orders for a second bookable offence.
Armed with a one-man advantage, Palace saw plenty of the ball after the restart but they were unable to find a way beyond Gilks in the home net.
Manchester United-bound Zaha looked the most likely to break the deadlock, but Gilks proved equal to his strike from distance just after the hour mark.
Their failure to make it count was punished as the match approached the 86th minute when Phillips kept his composure inside the area to beat Speroni and in doing so he sealed all three points for his team.