The Jacks failed to register at the Swedbank Stadion but dominated well enough to edge forward off the back of their 4-0 first-leg victory
A determined Malmo started the stronger of the two sides and went close to opening the scoring after only two minutes when youngster Pawel Cibicki fired just wide of the post.
However, Swansea soon showed the attacking prowess that helped them dominate the first leg, and they had the ball in the back of the net after 37 minutes when Wilfried Bony deftly placed his shot past Malmo goalkeeper Johan Dahlin, but the linesman's raised flag put an end to Swansea's celebrations.
Swansea boss Michael Laudrup decided to make seven changes to the side that thrashed Malmo 4-0 in the first leg, with only Ashley Williams, Wayne Routledge, Bony, and Michu being retained.
As for Malmo, manager Rikard Norling made three changes to last week's starting 11, with Erdal Rakip, Emil Forsberg, and Cibicki replacing Markus Halsti, Simon Thern, and star striker Tokelo Rantie.
A blistering start from the hosts led to the first chance of the game after only two minutes when Jiloan Hamad burst down the right wing before setting up 19-year-old striker Cibicki to fire just wide of Gerhard Tremmel's far post from the edge of the box.
Swansea found themselves on the back foot in the opening moments, but swift counterattacking play led to good chances in front of goal for Michu and Routledge, and the attacking confidence of a Swans side featuring several new faces seemed to grow as half-time approached.
Bony had the ball in the back of the net for the visitors after 37 minutes when he found himself on the end of a great pass forward from Routledge, but his soft side-footed shot past Dahlin was ruled out for offside, and it would prove to be the last real chance of the half.
The second half started in a more laid-back fashion than the first, but Swansea dominated proceedings and put pressure on a reserved Malmo side who seemingly had one eye on their important league clash against AIK on the weekend.
As the second half progressed, Swansea's dominance grew, and Jonathan De Guzman almost broke the deadlock for the visitors at the final moment when he poked the ball past Dahlin from close range. Pontus Jansson was there to clear the danger, however, and with it the final threat from a Swans side that proved they were far too strong for their opponents.