Larnaca stood alone as the only side yet to concede in a UEFA league phase so far this season, but their goal came under considerable threat in a mostly one-sided first half in Gothenburg.
Amor Layouni forced Zlatan Alomerovic into a save inside two minutes, while Isak Brusberg and Simon Gustafson went close in quick succession.
A quiet opening half-hour nearly saw the visitors snatch the lead against the run of play, with Jorge Miramon - who had assisted three match openers already this season - crossed to the back post where Giorgos Naoum headed on target only to be denied by a sprawling Silas Andersen block on the line.
Hacken recovered from that scare and resumed the mantle of the dictators of the contest, but they were unable to find a breakthrough before the break.
Brusberg released Adrian Svanback in behind on the stroke of HT, but Alomerovic responded well to rush out and smother the ball and provide the visitors with some welcome respite.
They utilised the break to that advantage, flipping the script after the restart to assert control on the contest. On the hour, Berisha was forced into his best save of the match, as he tipped over Djordje Ivanovic’s header from Miramon’s cross.
Having provided Larnaca’s most dangerous moments all night, Miramon stepped up to the plate to be the deadlock breaker.
He pounced on a tame Naoum shot and fired in at the near post with the help of a Filip Helander deflection, scoring a goal that always looked pivotal given his side’s imperious defensive record.
And the Cypriot rearguard looked to be holding firm, as did the crossbar when Hammar’s audacious lob had deceived Alomerovic. However, Hammar would have the last laugh, slamming home in the 94th minute to salvage a stalemate for the hosts.
Larnaca therefore spurned the chance to go top of the table despite their unbeaten away run reaching eight games, while Hacken may have done enough to keep their hopes alive on matchday six.