The Scots started with a massive pressure against MFF's goal and also received a dividend in the 19th minute when Alfredo Morelos kept himself ahead on a free kick.
The 1-0 goal means that right now it is extra time in the match.
Malmö has a 2-1 lead ahead of Tuesday's qualifier against Rangers at the classic Ibrox Stadium in Glasgow.
The winner of the doubles match - where the away goal rule does not apply - reaches the final qualifying stage for the Champions League group stage.
The match is in progress - the text is updated!