The Georgian side are unbeaten in the league in 2025, while Malmo have been struggling for form of late in the Allsvenskan, winning just one of their last five.
But domestic form went out of the window just eight minutes into the clash at the Mikheil Meskhi Stadium, when Malmo scored the first goal of the entire 2025/26 UCL season.
Oliver Berg's low strike was kept out by Giorgi Makaridze, but the goalkeeper could not stop the rebound falling to Busanello, who turned the ball home from close range.
Iberia had the better of the opening exchanges in the second half, but failed to conjure up a clear opportunity to get back on level terms.
That came back to haunt them just before the hour mark, when Malmo scored with the first effort on goal after half-time.
The ball was worked across the edge of the area to Daniel Tristan Gudjohnsen on the left - he then cut inside and caught the goalkeeper out by firing low towards the near post.
The hosts continued to have chances, only for Malmo to seal the healthy first-leg lead inside the final 20 minutes.
Taha Ali drove in from the left wing and left defenders in his wake as he dribbled along the edge of the penalty area before smashing the ball beyond Makaridze and into the roof of the net for a fine individual goal.
Iberia thought they had the chance to get back into the tie with 10 minutes to play when they were awarded a penalty, only for the referee to overturn his decision following a VAR check, deeming that Busanello had not committed a foul.
But the home side would not be denied the goal their performance arguably deserved - four minutes from time, a deep Luka Silagadze cross was headed home by Anes Rusevic for 3-1.
MFF will look to rubber-stamp their place in the Second Qualifying Round when they host the second leg next Tuesday.