The pressure was relentless from Chelsea; Catarina Macario fired home from close range, but once again the flag was raised for offside in the build-up.
However, the offside flag could not save Palace on 64 minutes as the hosts took the lead through James, who found the bottom-left corner with a volley from a half-cleared corner.
Despite taking the lead, the pressure did not lighten from Chelsea and Yañez was called into action again to deny Macario from close range.
Palace looked to find an equaliser at the death from a corner, but Sharpe couldn’t force her header goalbound and could only watch as it went out for a goal kick.
It wasn’t to be for the Eagles as one final chance from a free-kick was saved by Hampton, and Palace exited the FA Cup at the quarter-final stage.
Palace: Yañez (GK), Riley (Larkin, 52), Swaby, Gibbons, Woodham (Hughes, 80), Sharpe, Cato, Arthur, Blanchard, Weerden (Atkinson, 52), Larisey (Stengel , 78).
Subs not used: Majasaari (GK)
Chelsea: Hampton (GK), Lawrence, Bright, Bjorn, Baltimore, Cuthbert(Francois,74), Kaptein (Nusken, 45), Hamano (Kaneryd, 45), James (Charles, 83), Macario, Beever-Jones (Ramirez, 55).
Subs not used: Spencer (GK), Bronze, Brown, Jean, Fishel.