The Cottagers were held to a 1-1 draw at home to the Championship side but trailed 1-0 to Nathan Delfouneso's goal in the replay at Bloomfield Road.
However, Kieran Richardson sent the game into extra-time with a long-range effort in the 90th minute before the Norwegian ensured a trip to either Old Trafford or Upton Park in the fourth round when he met Damien Duff's cross.
|66/1||Fulham are 66/1 to beat Manchester City 2-0 with William Hill|
"In the first half we had two or three very good opportunities and you have to take pressure off your team. That is a responsibility you have got and that is what we lack sometimes."
Fulham travel to the Etihad Stadium to face Manchester City on Saturday before welcoming West Ham to Upton Park, with the Dutchman keen to distance his side from the Premier League trapdoor.
The Cottagers currently sit six points above the relegation zone after a dismal run of just two wins in 14 games.