Jessie Fleming’s first-half strike was all that separated the two sides, despite Chelsea dominating much of the game.
Fleming ran onto Ji So-yun’s ball after Elisha N’Dow struggled to intercept her pass and the midfielder kept her cool to finish past Hannah Hampton.
Ji and Erin Cuthbert both saw efforts hit the crossbar as the visitors looked to give themselves some breathing space but – in the end – a single goal was enough.
New Everton boss Jean-Luc Vasseur suffered defeat in his first league game in charge against Brighton.
Vasseur began his tenure with a win on Wednesday night against Leicester in the Continental Tyres League Cup after replacing Willie Kirk, but Aileen Whelan’s header inflicted a loss on the Frenchman’s team on Saturday.
Whelan had seen an earlier header hit the crossbar but she found the back of the net in the second half from Danielle Carter’s cross.
Everton’s best chances fell to Toni Duggan but on both occasions she put her efforts off target.
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