A Sandy Baltimore penalty on the stroke of half-time gave them a first-half lead, before Catarina Macario headed in the second in the 84th minute from a Baltimore free kick.
Baltimore sealed a fantastic performance by lashing the ball home from close range in first minute of stoppage time.
The victory means Sonia Bompastor’s side have added the FA Cup to their wins in the Super League and the League Cup.
The Blues have had an invincible season, going unbeaten across all three competitions.
It completes a memorable first season for the French manager, who took over from Emma Hayes when she went to manage the US national side.
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