AIK began the game knowing they had to win by at least two, as a one-goal victory would still see Hacken progress on goals scored.
By half-time, they didn't have a lead of any kind, but two yellow cards for Silas Andersen meant the holders were there for the taking, and the hosts finally made the breakthrough seven minutes after the restart through Zadok Yohanna.
The crucial goal arrived 20 minutes from time, and again it was Yohanna who provided the finish that took AIK's goal difference ahead of Hacken's.
One goal for the 10 men would still change everything, but only until the 89th minute, when Bersant Celina made it 3-0 to seal AIK's progression, before Erik Flataker made sure once and for all with another in added time, as AIK completed a 4-0 rout.
Vasteras SK began the evening with hopes of going through, only to fall to a 1-0 loss to Oddevold that confirms their third place in the group.
Last season's beaten finalists Malmo ensured they progressed to the last eight with a 2-1 win over Halmstad that sealed maximum points in Group 6, as Erik Botheim and Anders Christiansen struck either side of a Malte Persson leveller.
There were no issues for Allsvenskan champions Mjallby either, as they also won 2-1 at home to finish Group 1 on nine points, beating Varnamo thanks to two Jeppe Kjaer strikes either side of the break before Kai Meriluoto pulled one back.
Also joining the nine-point club, but in more impressive style, are Hammarby, who confirmed their place in the last eight by thumping Oster 7-0 in Stockholm, as Paulos Abraham and Wilson Lindberg both bagged a brace for the side whose 14 goals was the most scored across the Group Stage.
Second best with 12 were Sirius, but they only needed two away at Elfsborg to win the battle for first place in Group 8. Robbie Ure and Odera Samuel Adindu put the Uppsala side clear before Rufai Mohammed's goal made a game of it, but Sirius held on to win 2-1.
The tightest group was Group 5, which saw three sides finish on six points each, but coming out on top were Djurgarden, who won 2-0 at home to Brommapojkarna to overtake their opponents on goal difference, while a 3-2 win for Falkenburg over IFK Skovde was never going to be enough for the Superettan side to progress, despite beating Djurgarden earlier in the round.
In Group 4, Goteborg took just over half an hour to get the job done against Degerfors and hold off the challenge of Ostersund, as Max Fenger, Kolbeinn Thordarsson and Saidou Alioum put them clear before a late consolation wrapped up a 3-1 home win.
Across Gothenburg, GAIS are also celebrating safe passage to the quarter-finals, after a 5-1 win over Norrkoping saw them win Group 3 at a canter, as Kevin Holmen, Robin Frej, Joackim Fagerjord, Rasmus Niklasson and Shalom Ekong got on the scoresheet.
Svenska Cupen Quarter-finals
Seeded teams: Hammarby, Sirius, GAIS, Mjallby
Unseeded teams: Malmo, Goteborg, Djurgarden, AIK
Review all the results from the final round of Group Stage matches on Flashscore.
