The task was always going to be a difficult one for Hibs, who trailed by two goals from Jiloan Hamad and Magnus Eriksson following last week's meeting in Sweden.
Eriksson added to his goal from the first leg when he opened the scoring after 20 minutes, before a Rowan Vine effort was ruled offside for the Leith outfit.
There was a further setback when James McPake limped out of the action before the onslaught by the Swedes continued.
Emil Forsberg doubled the lead on the night on 25 minutes and Markus Halsti effectively ended the tie as a contest four minutes later.
But there was no let up from the visitors and Miiko Albornoz also added his name to the scoresheet four minutes before the break.
Tokelo Rantie helped himself to a goal on the hour mark, before Hamad scored five minutes later and substitute Simon Kroon completed the rout for the rampant Swedes on 72 minutes.
The emphatic win ensured Malmo progressed to a meeting with Swansea, ending any hope of a 'Battle of Britain' clash in the next round.
Ahead of kick-off, there was a minute of applause to celebrate the life and career of Hibs great Lawrie Reilly, who died earlier in the week.
Once the match was under way, Hibs actually started quite brightly and enjoyed much of the early possession, spurred on by a vocal crowd.
They had the chance to pile on the pressure with a corner of their own but Jordan Forster bulleted a header past the post from Liam Craig's delivery.
Then came a hint of what was to come in the shape of Eriksson's opener, as he pounced on Rantie's cross and rifled a low effort past the grasp of Ben Williams.
The goal appeared to spark the tie into life and Vine had the ball in the net for Hibs, with the offside flag already raised, before Rantie was denied at the other end.
The home side made their first change after 23 minutes when McPake was forced out of the action, making way for Fraser Mullen to make his debut.
It was one way traffic from then on, with Malmo grabbing the match firmly by the scruff of the neck.
Eriksson saw a shot smack off the post as he searched for a second, but it was Forsberg who netted for Malmo after exchanging a lovely one-two with Simon Thern.
Williams was left plucking the ball out of the net again when Halsti coolly dispatched a low shot from just inside the 18-yard box to ensure there would be no way back for their opponents.
There was to be no respite for Hibs in the first half and Albornoz was allowed to race unchallenged towards goal before sending a shot in off the post with half-time looming.
The second half was all about damage limitation for the Scots but there was further humiliation to come.
Rantie was quick to react after Williams parried a Hamad shot to pounce on the rebound and lash high into the net from close range after 60 minutes.
Five minutes later, Hamad drilled a low free-kick past the dejected Hibs goalkeeper from the corner of the 18-yard box.
By the end, Malmo were scoring for fun and Rantie demonstrated some decent play before cutting back for Kroon to stroke home on what was a night to forget for Hibs.