Fulham suffered a 2-1 defeat at home against Cardiff City on Thursday but advanced to next week’s Championship play-off final.
Curtis Nelson headed the visitors in front before Neeskens Kebano made it 1-1 on the night.
Substitute Lee Tomlin then put Cardiff back in front two minutes after the break, to set up a tense second half.
The Craven Cottage club had won the first leg 2-0 in Wales.
They will now face local rivals Brentford at Wembley, for a place in the Premier League.
Brentford on Wednesday beat Swansea City by the same aggregate score.
Fulham, who had finished one place above Cardiff in the final Championship table, last won a Championship play-off final two years ago, beating Aston Villa 1-0 at Wembley to earn promotion.
Brentford is looking to earn a spot in the top division for the first time in 73 years.