Rapid were happy to welcome first-leg absentee Mamadou Sangare back to the starting line-up, only for his night to last just seven minutes. Originally booked by referee Anthony Taylor for a poor challenge on Nino Zugelj, his punishment was increased to a red card after VAR intervention.
Santeri Haarala was brought on to replace the injured Zugelj, and he had the visitors’ first golden chance to benefit from their man advantage, but his effort at point-blank range was smothered by Niklas Hedl.
The home side took that as their signal to sit deep for the rest of the half and stifle Djurgarden. Yet, for the second time, VAR gave the Stockholm side a helping hand, deciding that Jonas Auer had handled the ball inside the area.
Marcus Danielson took responsibility for the spot-kick and sent Hedl the wrong way to give his side the lead on the night after 42 minutes.
However, the hosts would draw level within four minutes – a free-kick from the right was swung into a dangerous area, and the backtracking Jacob Une headed the ball into his own net to hand the aggregate lead back to Rapid.
Having conceded at home to Swedish opposition for the first time, only goal-line clearances from Serge-Philippe Raux-Yao and Dion Beljo on either side of half-time kept the Grun-Weissen from leaking further goals.
It wasn’t long before Beljo was having his customary chances at the other end, but was finding Jacob Rinne a tough opponent more than once as he searched for his sixth Conference League goal. Haarala had the chance to punish his lack of cutting edge on the hour mark, but his effort crept narrowly wide.
Matthias Seidl wasted the chance to put Robert Klauss’ team through when, somehow, he missed an open goal from six yards after Rinne palmed his first effort back to him, and Rapid were punished with 12 minutes remaining.
After a Tokmac Nguen curler was tipped over by Hedl, the resulting corner was half-cleared to Keita Kosugi, who swept the ball beautifully into the top corner.
There were late chances for the Iron Stoves’ August Priske and Adam Stahl, but another 30 minutes were required to separate the teams.
Extra time seemed to be too much for the 10 men, who caved after less than three minutes, when Nguen worked the ball across to Gulliksen, who unleashed a powerful 25-yard drive into the bottom corner.
On the stroke of half-time, Gulliksen all but settled matters, arriving late into the box and guiding the ball in off the post, having met Priske’s cutback.
That was enough for a fourth Conference League away win for Jani Honkavaara’s side, who will meet Chelsea in the semi-finals.
Meanwhile, Rapid’s misery was compounded when a bad tackle from Raux-Yao on Nguen saw them reduced to nine, as their wait for a first UEFA semi-final since 1996 continues.
Flashscore Man of the Match: Tobias Gulliksen (Djurgarden)