The Norwegian centre-back rose highest to nod home in extra time and seal a fourth round meeting with either West Ham or Premier League leaders Manchester United
The game had seen plenty of neat build-up play but little end product before Nathan Delfouneso pounced on a poor punch from Fulham goalkeeper Mark Schwarzer to tuck away what was seemingly a late Blackpool winner.
However, Kieran Richardson sent a fierce drive beyond Matty Gilks to take the tie to extra time and, after the home side missed a string of chances to win it, Hangeland headed home to setup a fourth-round clash with either West Ham or Manchester United.
The hosts' caretaker manager Steve Thompson had made two changes from the side which fell to defeat at Charlton Athletic on Saturday, with Kevin Phillips and Ludovic Sylvestre relegated to the bench in favour of Gary Taylor-Fletcher and Nathan Eccleston.
For Fulham, Martin Jol stuck by his pre-match promise to rest star players Dimitar Berbatov and Bryan Ruiz, as Hugo Rodallega and Ashkan Dejagah came in as two of five changes from the 1-1 draw with Wigan.
Both sides started in scrappy fashion, each giving away a succession of free-kicks, but Blackpool started to threaten through wingers Tom Ince and Ecclestone.
And it was more incisive wing-play that created the first chance for Ince, only for the Liverpool target to dither over his shot and allow Phillippe Senderos to make the block.
Berbatov’s omission had given Mladen Petric the opportunity to shine, but the Croat could only shank horribly wide after excellent work from Dejagah, as Fulham started to exert control over proceedings.
Shortly after, Gilks was drawn into action once more by Alex Kacaniklic whilst Chris Baird also saw a header shave the top of the bar as a largely forgettable first half drew to a frantic close.
Much like the first 45 minutes, it was the home side and Ince who came out of the blocks quicker but, having sprung the offside trap, the wideman could only direct a tame effort at Mark Schwarzer.
Both sides were playing with a lot more urgency in the second half and with nine minutes remaining on the clock, Blackpool eventually broke the deadlock.
Schwarzer flapped at a deep cross, only succeeding in punching it out to Delfouneso, who gleefully slammed home to spark wild celebrations at Bloomfield Road.
But the Tangerines’ hopes of a fourth-round berth were dashed in dramatic fashion as, deep into injury time, Richardson crashed in an unstoppable 25-yard effort to extend the tie.
Blackpool started the added 30 minutes the brighter and Schwarzer redeemed himself partly for his earlier gaffe by beating away Taylor-Fletcher’s follow-up to a low shot, before Kirk Broadfoot slammed a wayward effort way over the bar.
The home side continued to strive for the winner as, yet again, Ince failed to beat Schwarzer from close range, with the Australian pulling off a superb save to keep his side in it.
But Fulham repeated their trick of striking late when Hangeland looped a header over the unfortunate Gilks to break Blackpool hearts and seal a largely undeserved win.