The reigning Swedish champion club has had trouble with scoring goals in Allsvenskan.
In the 28-degree heat at the Micheil Meschi stadium in Georgia's capital Tblisi, the payoff came immediately. Already after just over eight minutes, Gabriel Busanello scored the leading goal.
The Brazilian kept himself forward when the home goalkeeper easily released a rebound on a shot from Oliver Berg.
MFF goalkeeper Melker Ellborg was involved in a situation that could have ended in a penalty for Iberia, but the referee judged after a video review that Ellborg was first on the ball.
In Malmö FF, central defender Pontus Jansson was back after his injury break.
Iberia was dangerous in their counterattacks, but lacked sharpness in the finishes. All the more precise was Daniel Gudjohnsen when he placed in 2–0 after 58 minutes.
Gudjohnsen was replaced by Taha Ali, who offered a really lovely 3–0 goal. A distinct shot up in one corner.
Anes Rusevic reduced in the final minutes.
The return match in the first qualifying round will be played at the stadium in Malmö on Tuesday next week.