Enzo Fernández proved the difference, heading home in the 23rd minute after connecting with a precise cross from Pedro Neto to give the Blues a first-half lead they would not relinquish.
Leeds threatened early, with Brenden Aaronson latching onto a flick from Dominic Calvert-Lewin, but Chelsea goalkeeper Robert Sánchez produced a vital save to keep the scores level.
Chelsea nearly doubled their advantage before the break when João Pedro struck the post, as both sides battled in a physical and closely contested encounter.
The win comes amid recent changes at Stamford Bridge, following the dismissal of manager Liam Rosenior, with Calum McFarlane currently serving as interim boss and now set to lead the team into the final.
For Leeds, the defeat ends hopes of a first FA Cup final appearance since 1973.
Chelsea will now face Manchester City in the final scheduled for May 16, setting up a high-stakes showdown between two of England’s top sides.
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