Back-to-back 3-1 victories in the First Qualifying Round over Georgian side Iberia 1999 had seen the Allsvenskan champions progress to face RFS, who beat FCI Levadia of Estonia 2-0 on aggregate.
Malmo were living up to their favourites tag within the first 13 minutes - RFS goalkeeper Marko Maric got down to deny Sead Haksabanovic, but could only palm the ball to the incoming Otto Rosengren, who gobbled up the rebound to open the scoring.
The Swedish side continued to have the better of the first half, as Jens Stryger and Rosengren both had opportunities to double the advantage, before the second goal finally came with 10 minutes of the half remaining.
At a corner, the RFS players left Pontus Jansson totally unmarked, and he didn't even need to jump to meet Busanello's delivery with his head and guide the ball past Maric.
But the Latvian side were not in the mood to roll over, and five minutes later they were back in the game. A corner was played short to Roberts Savalnieks, and his cross was perfect for Darko Lemajic to emerge from the crowded penalty area and head the ball past Robin Olsen.
In the second half, any hopes the home side had of completing the comeback failed to materialise and - in a professional performance - Malmo refused to let their opponents have a shot on goal.
MFF only had one effort on target of their own, but it was all they needed to seal the victory, just before the hour mark.
Hugo Bolin slipped an incisive a pass through to Haksabanovic and this time his strike was too good for Maric and Malmo.
The Swedish champions looked set for a third 3-1 win of the UCL Qualifiers until the final minutes, when Haksabanovic was brought down inside the area by Maric.
The goalkeeper went the right way from the resulting penalty, but Lasse Johnsen's spot-kick was too well placed, and Malmo were 4-1 up.
The Himmelsblatt may have one foot in the Third Qualifying Round, which will see them face either a local showdown with FC Copenhagen of Denmark or a trip to Kosovo to face Drita, but first they must come through unscathed from next Wednesday's second leg at home.