Goals at the end of either half knocked Mick Cooke's side out of the Europa League, following a credible scoreless draw in the first leg
The League of Ireland side showed resolve against the professional outfit but the Swedes took their chances while the Drogs failed to convert theirs.
Malmo coach Rikard Norling named Simon Thern in the starting line-up after he impressed after coming on as a sub last week. Mick Cooke drafted in veteran Declan O'Brien in place of the suspended Ryan Brennan.
The hosts dominated possession for large parts of the first half but as in Tallaght there was a lack of penetration in the final third. Indeed, it was the visitors who threatened first when David Cassidy looped a ball into the box which was palmed away by Johan Dahlin.
Malmo managed their first shot on target midway through the opening period when Magnus Eriksson fired a tame drive at Gabriel Sava.
Declan O'Brien almost put the travelling support in dreamland after he was put through by a crisp Cassidy pass. However, the striker was foiled by Dahlin who put his body between O'Brien and the goal.
The hosts became increasingly rattled giving the ball away and struggling to break down the determined Boynesiders. Just when it looked as though it would be scoreless at the break the home side struck.
Some neat interplay between Simon Thern and Tokelo Rantie allowed Emil Forsberg through on goal who clipped the ball cooly over Sava to put Malmo in front.
The tie should have been put to bed early in the second half when Tokelo Rantie was clean through only to miss from close range with the goal at his mercy.
Being in front gave MFF confidence as they sprayed the ball around with ease. They sought the second goal but despite long periods of pressure it wasn't forthcoming.
Drogheda grew tired as the second half wore on with Declan O'Brien looking isolated up front. Norling withdrew Thern for Erik Friberg to add some more experience in midfield.
Malmo should have added a second only for Paul O'Connor to make a crucial intervention. It looked like being 1-0 to the hosts but as in the first half Malmo left it late to grab a second.
As the Drogs pushed forward they left gaps at the back and it was left to substitute Simon Kroon to score from inside the box with an accurate finish to end the Louth side's European dreams for another year.
Malmo will now face Pat Fenlon's Hibernian in the Second Qualifying Round, with the first leg taking place in Sweden on July 18.