Malmo had already done the hard work a week ago, taking a 3-1 win away in the first leg in Tbilisi.
The Swedish champions were edging ever closer to a place in the Second Qualifying Round after they came through the opening 45 minutes unscathed - Iberia 1999 had five shots to Malmo's four, but neither produced anything to trouble either goalkeeper.
That all changed 10 minutes into the second half, as three incidents in a seven-minute spell won the match and the tie for MFF.
Lasse Johnsen slipped a pass through to set Taha Ali bearing down on goal, and he made no mistake dinking the ball over the goalkeeper to give Malmo the lead with his second goal of the tie.
It would have been 2-0 four minutes later had Giorgi Makaridze not made an excellent save to deny Daniel Tristan Gudjohnsen, but from the resulting corner, Pontus Jansson rose highest to head home Otto Rosengren's delivery.
Moments later, things went from bad to worse for the visitors when Gizo Mamageishvili was shown a straight red card for unsportsmanlike conduct to further hinder his side's chances of a comeback.
The hosts had further chances, with the pick of the bunch falling to Sead Haksabanovic, while Rosengren had a goal ruled out for offside.
But Rosengren would ultimately play a part in the Himmelsblatt's final goal - his pass found Ali, who in turn picked out the bottom corner to finish off a flowing team move.
The final word went to the Georgian side, who grabbed a consolation to through Amiran Dzagania after VAR confirmed he was not offside in the build up.
But with a 3-1 win in both legs, it's Malmo who progress to the Second Qualifying Round, where they will face Latvian champions RFS.
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