An error from debutant Sean Murdoch gave Dunfermline a mountain to climb after a Uefa Cup draw with Hacken.
Jonas Henriksson equalised for Hacken at East End Park
Pars striker Jim Hamilton scored after a minute of the first leg, pouncing after Sol Bamba's header hit the bar.
But Dunfermline lost goalkeeper Scott McKenzie and captain Scott Thomson to injury by half-time.
And replacement keeper Murdoch allowed a long ball to bounce over his head, leaving Jonas Henriksson to stroke the equaliser into the empty net.
The Swedes, who qualified for the tournament via the Fair Play process, had named veteran former Leeds United defender Teddy Lucic on their bench for the second qualifying round.
Dunfermline made three changes after a disappointing start to their First Division campaign - Hamilton, Stephen Simmons and Scott Wilson coming in for Stevie Crawford and injured pair Scott Muirhead and Tam McManus.
And the side relegated from the Scottish Premier League last season were one ahead after just 60 seconds.
Darren Young's whipped cross was cleared high into the air by defender Mats Heden and Hamilton nodded the ball home after a Bamba header struck the bar.
The Swedes responded and a powerful 30-yard free-kick from Brazilian Jose Antonio Pereira was well held by McKenzie.
But the goalkeeper almost gifted the visitors an equaliser seconds later when he kicked the ball straight against Dioh Williams following a Scott Thomson backpass.
McKenzie recovered to save but failed to shake off a thigh injury, limping off after diving to smother the ball at the feet of Daniel Larsson.
He was replaced with 21-year-old Murdoch, whose senior experience was during loan spells with Forfar Athletic and Hamilton Accies.
Jim Hamilton had given Dunfermline an early lead in Fife
Hacken attempted to put immediate pressure on the newcomer and Liberia striker Williams headed wide, forced the goalkeeper into a good save then sent a drive a few feet over.
The Pars were struggling to create any passing moves, although Bamba headed just wide from a Young free-kick.
Their cause was not helped by injury-prone defender Thomson, who had been struggling with knee injury, having to go off for Scott Morrison at the break.
Yet Hamilton had a chance early in the second half but struck the outside of the post from six yards.
And Simmons sent an effort inches over from 20 yards.
Just when Dunfermline looked like extending their lead, Murdoch's 57th-minute error handed the equaliser - and the initiative - to the visitors.
Murdoch redeemed himself with two good saves to deny the side relegated from Sweden's top flight.
And Bamba blasted well wide from 15 yards in the closing stages after late pressure almost gave Dunfermline an undeserved victory.
Dunfermline: McKenzie (Murdoch 9), Shields, Wilson, Young, Bamba, Scott Thomson (Scott Morrison 45), Simmons (Owen Morrison 78), Burchill, Hamilton, Harper, Glass.
Subs Not Used: McManus, McGuire, Crawford, Phinn.
Booked: Shields, Young.
Goal: Hamilton 1.
BK Hacken: Kallqvist, Lind, Heden, Marek, Ze Antonio, Williams, Mambo Mumba, Larsson (Olofsson 87), Skulason, Henriksson, Forsell.
Subs Not Used: Hysen, Ljung, Friberg, Holster, Lucic.
Booked: Marek, Williams.
Goal: Henriksson 57.
Ref: Robert Kranjc