Despite controlling possession, the Blues lacked penetration in the first half, failing to test Vicente Guaita in the Palace goal.
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Jefferson Lerma stunned the visitors with a thunderous strike, scoring his first Eagles goal to put the home side ahead.
However, the second half saw a more assertive Chelsea. On-loan loan star Conor Gallagher, tshot-takerfirst-half shot taker, smashed home the equalizer soon after the restart.
The game looked destined for a draw until a late Raheem Sterling counter-attack found substitute Cole Palmer.
His intelligent pass set up Gallagher for a second goal, shattering Palace’s hearts.
Enzo Fernandez added further gloss with a composed finish in the dying moments, sealing a hard-fought win for the visitors.