Pafos survived two major scares in the opening six minutes - Bruno Felipe completely stopped after thinking he was fouled by Oskar Fallenius, but the referee waved play-on before the winger's tame shot was routinely saved.
Then, Tokmac Nguen was far more clinical but saw his goal ruled out after handling the ball under pressure from Jonathan Silva.
Nguen’s frustration continued as Vlad Dragomir reacted brilliantly to block his shot after Jacob Une had nodded the ball down invitingly.
The visitors then had a positive spell of their own, although Derrick Luckassen couldn’t find the target following a pinpoint Ken Sema cross. Moments later, Ivica Ivušić rushed out to ensure a fortuitous bounce didn’t result in Nguen scoring as the home support at 3Arena grew increasingly disgruntled.
They had reason to celebrate in the 35th minute, though, as Fallenius linked up brilliantly with Nguen and poked the ball past Ivušić for his first-ever European goal.
Keita Kosugi then dinked in a dangerous cross but Adam Ståhl’s header directed the ball to Miro Tenho who couldn’t turn it towards goal.
Tobias Gulliksen thought he had put Djurgården ahead for the first time in the tie with an emphatic strike six minutes after the restart, but saw his goal ruled out after being adjudged to have fouled Silva beforehand.
The temperature soon rose and there were four yellow cards in 12 minutes - each meaning the recipient would miss the quarter-final if they progressed - and the teams had a chance apiece with Anderson Silva heading off-target before Fallenius hit the side netting.
Daniel Stensson then hit an audacious strike to put his side ahead in the 69th minute, although there was a blow shortly after as goalkeeper Malkolm Nilsson Säfqvist suffered a horrible injury.
After Fallenius’ effort was tipped onto the crossbar, Nguen headed home to make sure that Djurgården’s first win in four competitive matches came by a large enough margin to set up a UECL quarter-final against Rapid Vienna or Borac Banja Luka. In doing so, the Iron Stoves also ended Pafos’ memorable debut European campaign.