Malmo had already laid the groundwork a week prior, achieving a 3-1 victory away in the first leg in Tbilisi.
The Swedish champions were getting closer to a spot in the Second Qualifying Round after they completed the first 45 minutes without any issues - Iberia 1999 managed five shots compared to Malmo's four, but neither side was able to trouble the goalkeepers.
This changed dramatically 10 minutes into the second half, as three key events within a seven-minute span secured the match and the tie for MFF.
Lasse Johnsen delivered a pass that set up Taha Ali as he charged towards the goal, and he skillfully lifted the ball over the goalkeeper to give Malmo the lead with his second goal of the tie.
It could have been 2-0 just four minutes later if Giorgi Makaridze hadn't made a remarkable save to deny Daniel Tristan Gudjohnsen, but from the subsequent corner, Pontus Jansson rose highest to head in Otto Rosengren's cross.
Shortly after, the situation worsened for the visitors when Gizo Mamageishvili received a straight red card for unsportsmanlike behavior, further diminishing his team's chances of a comeback.
The hosts had additional opportunities, with the best chance falling to Sead Haksabanovic, while Rosengren had a goal disallowed for offside.
However, Rosengren ultimately contributed to the Himmelsblatt's final goal - his pass found Ali, who then struck the bottom corner to complete a well-coordinated team effort.
The last word went to the Georgian side, who netted a consolation goal through Amiran Dzagania after VAR confirmed he was not offside during the buildup.
But with a 3-1 victory across both legs, it is Malmo who advances to the Second Qualifying Round, where they will meet Latvian champions RFS.