Once again Peter Taylor played a different side in each half of the game, with a number of youngsters getting a slice of the action against a side managed by former Palace chairman Mark Goldberg.
However, Clinton Morrison and new signing Jeff Hughes both missed out as the pair are carrying groin injuries.
The match was goalless at half-time, but Palace took the league shortly after the break courtesy of an own goal following a Green corner.
But Bromley turned the match on its head with two goals in three minutes just before the hour mark.
Palace kept piling on the pressure, and they were rewarded in the final minute as Green rifled home.
First half
Flinders, Butterfield, Craig, Hudson, Swaibu, Grabban, Kennedy, Freedman, Kuqi, Kudjodji, Hall
Second half
Speroni, Lawrence, Wiggins, Cort, Fletcher, Watson, Green, Soares, Scowcroft, Ifill, Martin