Aberdeen are two ties from the Europa Conference League group stage after surviving a fightback by BK Hacken to progress despite defeat in Gothenburg.
Leading 5-1 from the first leg, the Scottish side went behind when Martin Olsson slotted home for the hosts.
Leo Bengtsson converted from the spot to pile the pressure on, but Patrik Walemark's red card with 20 minutes left helped Aberdeen hang on.
They face Breidablik next after the Icelandic side stunned Austria Vienna.
Pre-match Stephen Glass said he would not be rotating his squad with Sunday's Scottish Premiership opener against Dundee United in mind, despite such a commanding lead.
Clearly looking to build momentum and cohesion, he stuck to his words and picked the same XI that took the Swedes apart at Pittodrie.
But, as in the first leg, Aberdeen made a shaky start, with Ross McCrorie blocking an early effort and Tobias Heintz rattling the outside of a post.
However, the visitors settled into the game and created the better chances in the first half, as Jay Emmanuel-Thomas and Christian Ramirez forced Peter Abrahamsson into good saves.
That dominance seemed to kill Hacken's spirit, but Olsson's clever one-two and finish into the corner revived Swedish hopes early in the second half and they set about trying to unnerve Aberdeen.
Funso Ojo should have ended any doubt about the outcome of the tie just four minutes later, but he failed to connect with Ramirez's cross with the goal gaping.
And worse was to come when substitute Nasiru Mohammed slid a pass through to Bengtsson, who was tripped by Joe Lewis before stepping up to send the goalkeeper the wrong way.
Both sides lacked cohesion defensively and the game opened up, before a creaking Aberdeen side were handed a lifeline when Walemark was sent off after getting a second yellow card for connecting with Jack Mackenzie's face.
It was a dubious call and it killed the Swedish side's momentum as Aberdeen were able to steady themselves and crucially finish the job.
Man of the match - Nasiru Mohammed
Mohammed came on just before the break and caused Aberdeen's centre-backs problems by dropping off, with his pass leading to the penaltyWhat did we learn?
Aberdeen look a completely different team to last season. They press high up the pitch as a unit, the full-backs join the attack and Emmanuel-Thomas provides a platform for them to play off going forward as runners come from deep.
The best of all those things was in evidence in the first leg as they ripped through Hacken, and they put in a similar display for large spells of the opening half in Gothenburg.
However, defensively this week they looked far more shaky. In their keenness to win possession up the pitch, players dived into tackles which allowed Hacken to play into midfield at times, where there was too much room. McCrorie in particular was caught out by long balls into the channels.
And, when Emmanuel-Thomas departed early in the second half with a head injury, the attack suffered in his absence. His link-up play is crucial to bringing other players into the game.
Overall, though, Glass will be pleased to have negotiated a tricky tie, and will expect greater cohesion to come in time.
What they said
Aberdeen manager Stephen Glass: "I don't think it got to the stage of nervy but it was a bit more frantic at the end than we would have liked.
"We had chances in the first half that would've killed it. I think what you saw tonight was a Hacken team playing carefree - and any team playing like that can be dangerous."
What's next?
Aberdeen open their Scottish Premiership campaign at home to Dundee United on Sunday (15:00 BST) as they look to build on European progress.
Line-ups
BK Häcken
Formation 4-3-3
26Abrahamsson
5Ekpolo22Carlsson3Hammar15Olsson
17Berggren6Faltsetas11Heintz
16Traore9Jeremejeff7Bengtsson
26Abrahamsson5Ekpolo22Carlsson3Hammar15OlssonSubstituted forSverrissonat 76'minutes17BerggrenSubstituted forMilovanovicat 80'minutes6Faltsetas11HeintzSubstituted forMaaroufat 80'minutesBooked at 90mins16TraoreSubstituted forWalemarkat 45'minutesBooked at 71mins9JeremejeffSubstituted forMohammedat 40'minutesBooked at 73mins7BengtssonSubstitutes
1Brattberg12Fridriksson13Adjoumani14Sverrisson23Walemark24Milovanovic27Farah Shahin28Maarouf29Rasheed32MohammedAberdeen
Formation 4-4-2
1Lewis
22Ramsay2McCrorie4Considine17Hayes
11Hedges19Ferguson8Brown16Ojo
14Emmanuel-Thomas9Ramírez
1LewisBooked at 67mins22RamsayBooked at 79minsSubstituted forGurrat 82'minutes2McCrorie4Considine17HayesBooked at 54minsSubstituted forMacKenzieat 66'minutes11HedgesBooked at 70minsSubstituted forGallagherat 83'minutesBooked at 76mins19Ferguson8Brown16OjoSubstituted forMcLennanat 66'minutes14Emmanuel-ThomasSubstituted forJenksat 50'minutes9Ramírez