Both sides were in need of the win if they were to harbour any real hopes of reaching the knockout stages, but in windy conditions, the first half was anything but a classic as both sides struggled to exert any sustained pressure.
Having failed to score in either of their past two games in this competition, the hosts almost ended their drought when Mario Cuze was played in on goal, but from a tight angle, he got his attempt at a delicate chip all wrong, allowing the visitors to clear.
The Swedes had not looked like scoring throughout the first half, yet they found the opener from nowhere shortly before the break. Mikkel Rygaard was the architect, curling a delightful cross onto the head of Silas Andersen, who nodded past Marin Ljubic between the Zrinjski sticks.
That goal breathed life into Häcken, and only the post prevented Rygaard from finding the top corner with a lovely strike as the away team aimed to force home their advantage.
After the interval, Hacken were the dominant side, going close to extending their lead on several occasions. Fed by Rygaard, Simon Gustafson could only slice wide from inside the penalty area, before Amor Layouni’s overhead kick was pushed over by Ljubic.
Andersen had perhaps the best chance, somehow poking past the post from just a few yards out. At the other end, Nemanja Bilbija couldn’t quite get a ball over the top under control with just Hacken shot-stopper Etrit Berisha to beat.
That was one of the few noteworthy forays forward, and they did not look like equalising until the 78th minute. Berisha was equal to Cuze’s first strike, but could only parry straight into his path once more, and the Croatian was in no mood to waste the opportunity a second time.
Buoyed by that effort, Zrinjski immediately appeared to be in control of the game, and were soon in front courtesy of a fantastic strike as Bilbija arrowed a half-volley in off the post from all of 30 yards.
Hacken looked shell-shocked, and while the onus was on them to salvage something, they could not produce anything of note.
The result leaves Hacken in a difficult position, with just two points to their name from four matches, while Zrinjski now look relatively comfortable in the play-off places, and will believe a spot in the knockout stages is a realistic possibility.
Flashscore Man of the Match: Nemanja Bilbija (Zrinjski)