After Ludovic Sylvestre opened the scoring for the Championship outfit, the Greek international averted an upset with a stunning effort as a replay beckons for both sides
After a goalless and relatively chance-free first half, Sylvestre opened the scoring with a right-footed strike from the edge of the area as Fulham appealed vehemently, and unsuccessfully, for a handball against Kevin Phillips.
Karagounis spared the Premier League side's blushes with a stunning finish from the edge of the area before Bryan Ruiz almost won it right before the death, only for his header to be cruelly denied by the crossbar.
Jol decided to forgo rotation as he made no changes to the side that beat West Brom 2-1, meaning the Blackpool defence had to contend with the dual threat of Ruiz and Dimitar Berbatov all afternoon.
In contrast, the Championship outfit rang the changes, bringing in Bob Harris, Phillips and Nathan Delfouneso with Stephen Crainey, Gary Taylor-Fletcher and Wes Thomas all departing from the side that drew 0-0 with in-form Hull earlier this week.
After a fairly even, albeit fairly eventless, start, the first clear-cut chance fell to Blackpool's Thomas Ince. After good work from Chris Basham down the left, the diminutive winger fired at goal from 10 yards out but David Stockdale was equal to his effort.
Fulham started to assert themselves on the game with the 20 minute mark approaching, as two chances fell to the Premier League side in quick succession - Ruiz first forcing a good save from Matt Gilks from a free kick and Dejagah then spurning a chance after good wing play from Alex Kacaniklic.
In spite of the Cottagers' mounting pressure, the next chance fell again to Ince, who tested Stockdale with a powerful right-footed effort but, once again, the Fulham goalkeeper produced a good save to keep the tie goalless.
From then on, the game evened out with half-chances falling to either side, with Phillips and Briggs both missing chances before the interval.
The second-half carried on much in the same vein up until the 60th minute when, controversially, the away side took the lead.
With Fulham still appealing for a handball from Phillips, Delfouneso attacked down the left, cut inside and laid the ball off to Sylvestre. The Blackpool midfielder made no mistake in finishing from just outside the area, striking into the bottom corner with aplomb.
With the hosts struggling to mount any real response to the goal, Blackpool still seemed more likely to score as Ince very nearly managed to get himself on the end of a dangerous Eardley cross.
It took Fulham until the 80th minute to finally respond, but they did it in some style as Karagounis levelled with a stunning effort. The Greek international picked the ball up on the right flank before cutting on to his left foot and curling a fine finish over the helpless Gilks to cancel out Sylvestre's earlier strike.
The Cottagers' Premier League status began to tell following the goal as Kieran Richardson went mightily close with a right-footed effort after cutting in from the left flank, dragging the ball just wide with five minutes remaining.
Ruiz went even closer two minutes later as, following a cross from Frei, his stooping header flew past the goalkeeper but was denied by the crossbar, and the Cottagers must now prepare themselves for a replay.