The Welsh club had held a 4-0 lead coming into the second leg of this third qualifying round tie and Michael Laudrup's side were rarely troubled as they advanced with ease at the Swedbank Stadion.
Wilfried Bony, the two-goal hero last week, had the ball in the net again this week but was denied by an offside flag, while Michu, Wayne Routledge and Jonathan de Guzman failed to finish good chances.
Malmo's best chance came inside 90 seconds, but Pawel Cibicki fired wastefully wide as they exited the tournament tamely.
Having survived that early scare, Swansea quickly took control of proceedings.
Alejandro Pozuelo freed Michu but the Spaniard's sliding left-footed shot was foiled by the quickly advancing Johan Dahlin.
Routledge failed to convert a better opportunity just a few minutes later. Jose Canas' lovely lofted pass sent the winger racing through on goal but he prodded a right-foot effort wide of the far post.
Bony showed them how it should be done with a clinical finish from a Routledge through-ball, but the Ivory Coast international was adjudged to have strayed beyond the last defender.
In truth Swansea never threatened to reach the level of performance shown in the first leg, but they thought they had the goal their dominance merited late on in a forgettable second half.
Pozuelo's chip played in De Guzman and the Dutch international nicked the ball past Dahlin, only for Pontus Jansson to recover and clear off the line.
It was Europa League misery though for Motherwell who crashed out after a 1-0 defeat in Russia to Kuban Krasnodar.
The Lanarkshire side were relatively comfortable, without having seriously threatened to cut their 2-0 first-leg deficit, before McManus headed into his own net five minutes into the second half.
Motherwell, who were without three key attacking players, had the perfect chance to level in the final minute after Djibril Cisse handled Stevie Hammell's free-kick but substitute McHugh saw his effort saved.
Their small band of fans at least had something small to celebrate when Gunnar Nielsen marked his debut with a 75th-minute penalty save from Charles Kabore.
St Johnstone waved goodbye to their 42-year unbeaten home record in European competition as FC Minsk claimed a penalty shoot-out victory to end their Europa League hopes.
Milnos Rnic struck the only goal of the game for the visitors after 75 minutes but Saints clung on through extra time to take the third qualifying round encounter to the spot-kick decider.
Skipper Dave MacKay and Paddy Cregg missed the Scots' first two attempts but salvation looked to be on the cards when Alan Mannus saved successive attempts by Vital Kibuk and Siarhei Kazeka to level it 2-2.
But Steven MacLean saw his decisive penalty stopped by the Belarusians' number one Vladzimir Bushma to end the Perth men's hopes of landing the £1.1million windfall that comes with a place in the group stages.