The Norwegian center back rose highest to nod home in extra time and seal a fourth-round FA Cup meeting with either West Ham or Premier League leader 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.
Kieran Richardson sent a fierce drive beyond Matty Gilks to take the tie to extra time, though, and after the home side missed a string of chances to win it, Hangeland headed home to set up a fourth-round clash with either West Ham or Manchester United.
Both sides started in scrappy fashion, each giving away a succession of free-kicks, but Blackpool started to threaten through wingers Tom Ince and Nathan Ecclestone. It was more incisive wing play that created the first chance for Ince, only for the Liverpool transfer target to dither over his shot and allow Phillippe Senderos to make the block.
Dimitar Berbatov’s omission had given Mladen Petric the opportunity to shine, but the Croatian could only shank wide after excellent work from Ashkan Dejagah, as Fulham started to exert control over proceedings.
Shortly after, Gilks was drawn into action once more by Alex Kacaniklic, while Chris Baird also saw a header shave the top of the bar as the first half drew to a frantic close.
Both sides played with a lot more urgency in the second half, and with nine minutes remaining, 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.
The Tangerines’ hopes of a fourth-round berth were dashed in dramatic fashion, though, 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 Gary 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. Fulham repeated its trick of striking late when Hangeland looped a 116th-minute header over the unfortunate Gilks to break Blackpool's hearts and seal the victory.