The result was far removed from Mjallby's domestic form - the Allsvenskan champions had drawn four and lost two of their last six league games, which would have given Lincoln Red Imps real belief of causing another upset to add to their European collection.
But Mjallby took control of the game 18 minutes in, when Jeppe Kjaer tried his luck from 25 yards and his strike was batted away to Aki Samuelsen on the left. He cut into the area and sent a curling effort past Jaylan Hankins with the help of a fortunate bobble.
The home side doubled their lead six minutes later with a wonderful team goal - Kjaer, Viktor Gustafson and Jesper Gustavsson were all involved in an intricate passing move outside the Red Imps box before slotting through to Samuelsen to steer home his second.
The visitors then failed to make the most of a good spell of pressure, and MAIF punished them when Villiam Granath found Jacob Bergstrom inside the box, and the local cult hero made space for himself and striking into the bottom corner to add his name to the score sheet.
Mjallby should have put the tie to bed, but Kjaer fired narrowly wide on the stroke of half-time, then midway through the second half, Samuelsen missed the chance to complete his hat-trick when Mjallby won themselves a penalty. Hankins saved the spot-kick, before Elliot Stroud struck the rebound against the crossbar.
Those misses keep the tie alive for the Gibraltarian side, who will host the second leg on 28th July.
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