The result earns Palace their first ever win in the WSL and indeed English Women's football's top-flight.
Next up is Brighton & Hove Albion at the VBS Community Stadium on Sunday, 13th October (14:00 BST). Tickets are available for that fixture here.
Leicester: Leitzig (GK), Tierney, Bott, Howard, Takarada, (Chossenotte, 46) , Rantala, Mouchon, Cayman, Thibaud, Goodwin (Momiki, 56), Mace.
Subs not used: Kop (GK), Nevin, Rose, Pelgander, Kees, Swaby, Las.
Palace: Yañez (GK), Everett, Veje, Woodham, Green, Cato, Gejl (Riley, 74), Potter, Blanchard, Weerden (Larkin, 57), Stengel.
Subs not used: Majasaari, Gibbons, Arthur, Sharpe, Riley, Aspin, Atkinson.