A fine team performance and some strong defending late on from Michael Appleton's side mean Blackpool's name will be in the hat for the fourth round of the FA Cup.
It could have been so much better for The Seasiders had Giorgos Karagounis' volley ten minutes from time not cancelled out Ludovic Sylvestre's 60th minute strike.
The early stages were largely uneventful until the seventh minute when Dimitar Berbatov threatened to latch on to a chipped ball into the box only for Alex Baptiste to intervene and turn the ball behind for a corner.
The first real chance fell to Blackpool though when some neat play from Sylvestre and Chris Basham helped to tee up Thomas Ince, whose shot was tipped over by David Stockdale.
Ince then let fly with another effort from an acute angle but his shot was blocked by the shins of Brede Hangeland this time.
The Cottagers then began to impose themselves on the game following The Seasiders' strong start and Askan Dejegah was inches away from giving his side the lead but he volleyed narrowly wide from eight yards out.
After around 30 minutes it was still goalless and Blackpool threatened once again when Kevin Phillips squared the ball for Ince who checked back onto his right foot before stinging the palms of Stockdale.
Phillips was the next to try his look when he received the ball 30 yards out and with only one thing on his mind he struck a rasping drive, which Stockdale saved low down to his left.
HALF-TIME: FULHAM 0-0 BLACKPOOL
The Seasiders started the second-half confidently and despite Martin Jol introducing Hugo Rodallega early on it was Blackpool who took the lead through Sylvestre.
GOAL: Fulham 0-1 BLACKPOOL
The goal came when Sylvestre played a defence splitting ball for Delfouneso to run onto before he squared the ball across the edge of the box for the midfielder to fire home first time from 20 yards out.
The Seasiders had to withstand some heavy pressure following the goal but some timely interventions from Bob Harris and Kirk Broadfoot frustrated the home side.
With Fulham pressing a quick counter-attack set Ince away down the left but his low driven cross evaded everyone and went behind for a goal-kick.
Another counter-attack moments later gave Bob Harris the opportunity to let fly from 25 yards but his cross come shot whistled beyond Ince and the far post.
With just ten minutes to go Fulham equalised thanks to a superb volley from Karagounis, which dipped into the far corner giving Gilks no chance.
GOAL: FULHAM 1-1 Blackpool
The goal certainly spurred The Cottagers into life and they almost got a second but Bryan Ruiz's header thundered back off the crossbar from Kerim Frei's left-wing cross.
The Seasiders saw out the final stages with some masterful defending meaning a replay will have to settle this tie.
FULL-TIME: FULHAM 1-1 BLACKPOOL