In a rematch of last year's final that they lost 1-0, Marc Skinner's United went in front in the first minute through a Lucia Garcia header before doubling the advantage midway through the first half when Rachel Williams headed home.
Former United player Lauren James pulled a goal back just prior to the break and the visitors did most of the attacking thereafter but were unable to force extra time, with Mary Earps making a superb save to thwart James and substitute Catarina Macario hitting the bar.
The result is a first victory for United over Chelsea since the team's launch in 2018 and they now have a chance to secure a maiden piece of major silverware when they return to Wembley on May 12 to face Spurs, who beat Leicester in the other semi-final earlier yesterday.
Chelsea, meanwhile, saw a trophy bid end for the second successive game, having lost 1-0 to Arsenal in the League Cup final last time out.
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