Hangeland was part of the defence, including goalkeeper Mark Schwarzer, that kept out almost everything the Ukrainians threw at them at the vast Donbass Arena.
And Hangeland also popped up with Fulham's goal in the 33rd minute - with virtually their first attack of the night - to set up a stunning success for Roy Hodgson's men.
They had to withstand immense pressure in front of a vociferous home crowd but finally got breached in the 69th minute when Jadson fired Shakhtar level.
Fulham held out for the final, nerve-jangling last 20 minutes, though, to knock out the 2009 UEFA Cup winners and make the last 16 of the revamped competition for the first time in their history.
Only a stoppage-time red card for Danny Murphy, which will rule him out of their next match, marred a memorable evening in Donetsk.
Shakhtar, who had Luiz Adriano's away goal to show for their efforts in the first leg at Craven Cottage, were quickly into their stride with their five-strong Brazilian contingent looking sharp.
Schwarzer comfortably dealt with a low shot from Adriano in the opening minute but he was called into more serious action just two minutes later when he tipped a long-range effort from Willian over the crossbar.
Adriano should have done better with an attempted curler moments later but then, with the visitors retreating deeper and deeper, Schwarzer kept his side on level terms with a superb diving one-handed save to deny Fernandinho.
Fulham's overworked keeper then had to block another low Willian drive midway through the first half and it was all hands to pump in the visitors' box with striker Bobby Zamora hacking a dangerous low centre clear before Schwarzer scrambled Yaroslav Rakitsky's 30-yarder round a post.
But having stood up to the barrage, incredibly it was Fulham who took the lead in the 34th minute.
Zamora won a free-kick down the right, Damien Duff floated in the cross and Hangeland's glancing header beat the motionless Shakhtar goalkeeper Andriy Pyatov.
It cancelled out Adriano's strike seven days earlier, to the delight of 350 hardy travelling fans, and meant Shakhtar needed to score twice to stay in the tie.
The hosts were straight back on the attack after the break, however, and Adriano headed captain Darijo Srna's cross into the arms of Schwarzer.
But although Shakhtar continued to dominate, Hangeland was imperious at the back, cutting out a driven centre from Razvan Rat with an immaculate first touch and getting his head onto just about everything else thrown at him.
With frustration growing in the home ranks, substitute Douglas blazed an ambitious 25-yarder high over Schwarzer's crossbar.
The Cottagers had a chance to kill off the tie when a rare counter-attack saw Zamora break clear down the right but his square cross, towards an unmarked Zoltan Gera, was cut out by defender Olexander Kucher.
And the moment Fulham feared came in the 69th minute when Douglas reached the byline and pulled the ball back for Jadson to sweep past Schwarzer to level the match on the night.
Fulham hearts were in their mouths with 10 minutes to go when a vicious curler from defender Rakitsky thundered into the side-netting.
Then Douglas' shot was deflected wide off Murphy with Shakhtar screaming for handball.
Gera passed up another chance to put Fulham clear when he scuffed wide in the final minute, before Murphy was shown a red card for kicking out at Srna moments before the final whistle.
It did not matter, though, as the Cottagers held on for a famous success.