Almost a minute after going in front, Palace claimed a two-goal cushion with Drakes-Thomas pushing on and slotting home.
It was all Palace in the final 20 minutes of the game, with Williams crashing an effort off the crossbar, following great build-up play with Derry, and Benamar fired a volley just over.
The young Eagles saw off nine minutes of time added on and any late Chelsea resurgence to claim all three points to end the year in style. The result means Quinn and his side move up to fifth in the table, level on points with Fulham in third place.
**Palace:** Hill (GK), Okoli, Benamar, Adams-Collman (Oduro, 90+1), Somade, Fasida, Drakes-Thomas, Henry (Judd, HT), Casey (Osei, 90+5), Williams, Derry.
Subs not used: Whitworth (GK), Cowin.
**Chelsea:** Bernal (GK), Wheeler-Henry (McGlinchey, 71), Subuloye, Emenalo, Antwi, Harrison, Runham, Nutter (Washington, 81), Ezenwata, Walsh (Rabbaj, 87), Barbour (Idrissi, HT).
Sub not used: Collinson (GK).