An entertaining game was decided by a Yann Kermorgant penalty, after Tomas Kalas handled inside the area.
The 35-year-old striker plans to retire at the end of next season and could well be showcasing his talents in the Premier League
There was little to separate these two sides in the first leg, which finished 1-1 at Craven Cottage on Saturday, and ultimately it took a mistake to settle the tie.
Fuham defender Kalas was the fall guy as he stuck out an arm to control the ball, allowing Kermorgant to drill home from the spot.
Fulham were a threat throughout but did not test Ali Al Habsi enough over either leg and go down 2-1 on aggregate.
Reading will now face either Huddersfield or Sheffield Wednesday, who play on Wednesday after a goalless first leg.
The Championship Play-Off final takes place on Monday, May 29.
