The Boynesiders lined out with their talismanic winger Gavin Brennan at left-back, while Alan Byrne sat in front of the back four for added protection.
And for long spells in the first half, the defensive approach served Drogheda well as they stood firm and prevented the Swedes creating any clear-cut opportunities.
After a quiet opening six minutes, the hosts brought the tie to life when Gavin Brennan collected a David Cassidy pass and whipped in a cross where Paul O’Conor just failed to get a touch ahead of keeper Johan Dahlin.
For the next 15 minutes Malmo played some tidy football near the Drogheda box but couldn’t find a pass to break through a solid rearguard, and their South Africa international striker, Tokelo Rantie, was fortunate to stay on the field after going in high on Derek Prendergast.
Malmo had another lucky escape when Peter Hynes released David Cassidy through the centre and keeper Dahlin’s attempted clearance ricocheted off Erik Johansson towards goal before being scrambled clear.
Byrne almost broke the deadlock on 55 minutes following one of the those fouls when he met Cassidy’s far-post free kick with a header which landed on the roof of the net.
And only for poor control by O’Conor in the Malmo six-yard area, the midfielder could have scored from close range from a Michael Daly cross.
But Drogheda’s chances of taking a result to Sweden next week were dealt a severe blow on 75 minutes when Ryan Brennan, having already been booked for dissent, brought down Rantie and earned a second yellow card from the Bosnia & Herzegovina referee.
After that it was backs to the wall for the League of Ireland side, and Sava earned his corn on 87 with a great save from Rantie.
DROGHEDA UNITED: Sava; Daly, McNally, Prendergast, G Brennan; Byrne; Cassidy, O’Conor, R Brennan; O’Neill, Hynes.
Subs: O’Brien for O’Neill (67min), Gannon for Hynes (79min).
MALMO: Dahlin; Albornoz, Jansson, Johansson, Ricardinho; Hamad, Friberg, Halsti, Forsberg; Rantie, Eriksson.
Subs: Thern for Forsberg (55min).
Referee: Emir Aleckovic (Bosnia & Herzegovina).