The Seasiders looked set to add another memorable chapter to their cup folklore - almost 60 years after Sir Stanley Matthews inspired their sole triumph - when Ludovic Sylvestre gave them a shock lead at Craven Cottage.
Veteran Greece midfielder Karagounis rolled back the years with a stunning half-volley after Fulham lay siege to the visitors' goal but Martin Jol's men have it all to do to avoid Blackpool completing the upset at Bloomfield Road.
This year marks the 60th anniversary of the 'Matthews Final', one of the most celebrated cup finals of all time. But it was the Seasiders' current 'Wizard of Dribble' who was the name on everyone's lips at Craven Cottage, with Thomas Ince starting despite reportedly being on the brink of rejoining Liverpool.
Alex Baptiste was in the thick of it early on, beating Dimitar Berbatov to Karagounis' fine ball only to almost turn it past his own goalkeeper. And it was not long before Ince got in on the act, blasting too close to David Stockdale from close range after a neat 13th-minute move and lay-off from Chris Basham.
Sylvestre was thwarted by Steve Sidwell's desperate tackle before a lovely backheel from the recalled Kevin Phillips set up Ince for another drive Stockdale could only palm behind.
The home inside upped the tempo after the break but their dominance was an illusion as Blackpool broke out to take the lead just before the hour mark. Nathan Delfouneso had just seen a penalty appeal turned down when he again found himself on the left edge of the area, this time picking out Sylvestre, who rifled a low 18-yard drive into the corner of the net.
The visitors were looking a real threat on the break as time ticked down for the home side, who were in need of a moment of inspiration. It finally arrived with 10 minutes remaining and it was worth waiting for.
Blackpool thought they had cleared a corner but they did not reckon with Karagounis, who controlled the ball before unleashing an unstoppable dipping half-volley from the corner of the area, which sailed over the helpless Gilks. It was Karagounis' first goal for the club and arguably one of the best of the season.
It could easily have been followed by a winner but Bryan Ruiz's header against the crossbar from Kieran Richardson's cross and an amazing stoppage-time miss - seemingly by Hugo Rodallega - from a corner.