After a steady start, the visitors burst into life around the 15-minute mark. Romeo Amane had their first real chance, pouncing onto an under-hit back pass and forcing a superb save out of Jacob Rinne, who then made an impressive stop from Isak Jansson.
At the other end, Niklas Hedl raced quickly off his line to block Oskar Fallenius’ stabbed effort from point-blank range as the two teams traded blows.
As the game wore on, the Iron Stoves, hunting a fourth straight home win in this competition, were increasingly threatening, with Fallenius wasting another chance as his quick break and prodded effort was diverted to safety.
The winger had now shown his hand though, meaning the Green and Whites were aware of the danger he posed, and as such afforded him little space over the remainder of the half, quickly snuffing out any danger.
The second half continued in a similar fashion, with openings of sparse supply, but when they came, they were clear-cut chances.
August Priske had one for the hosts, but he was guilty of sending a free header from a free-kick way off target, before Robert Klauss’ side took the lead when Hampus Finndell inadvertently diverted Louis Schaub’s drilled cross past his own goalkeeper.
Djurgarden, who were in their first European quarter-final, could have responded almost immediately when Fallenius’ fizzing strike from distance deflected wide, while he also sent a 25-yard strike off target.
There was to be no equaliser though, as the Swedish side failed to score for the second home game running, whereas Rapid ended a run of back-to-back 2-0 defeats.
Flashscore Man of the Match: Louis Schaub (Rapid Vienna)