Yann Kermorgant's penalty just after halftime proved decisive as Jaap Stam's Reading held firm on a tense night.
Reading will face either Sheffield Wednesday or Huddersfield Town in the Wembley final to decide which club joins Newcastle United and Brighton and Hove Albion in the top flight.
Frenchman Kermorgant, 35, coolly fired home from the spot after Fulham centre back Tomas Kalas was penalised for handball.
It was his 19th league goal of the season.
Fulham had dominated before the break and Reading were indebted to Oman international keeper Ali Al Habsi who made a fine double save to deny Tom Cairney's curling free kick followed by Sone Aluko's rebound.
He also touched a Ryan Fredericks shot on to the post.
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