Visiting Granada, who finished seventh in La Liga last season, took the lead after half an hour.
Venezuelan Darwin Machis was released after a nice action by Antonio Puertas, and put 1-0.
It lasted until the last minute of the first half.
If it had been an audience, it would have cheered then because Malmö equalized.
Jonas Knudsen was responsible for a long throw, which was spliced in the post by a Granada player and then Jo Inge Berget was in front and put in the rebound.
Overall, it was the Spaniards who led the game in the first half, but in terms of chances, MFF kept a steady pace.
Great opportunity to acknowledge
Barely a quarter into the second, Puertas was involved again when Granada regained the lead.
He got the ball in the penalty area and placed it safely behind Marko Johansson.
Just minutes later, MFF's midfielder Anel Ahmedhodzic should have equalized when he Erdal Rakip hit a perfect free kick into the penalty area.
After a short tussle with the defender, Rui Silva finally tucked the ball home.
Instead, the stroke of mercy came with six minutes left of regular playing time.
It was a similar situation to the one that Ahmedhodzic missed, but Yangel Herrera put the ball in for 3-1.
Malmö has played Europa League group games two seasons in a row, but this year there will be no Swedish team at all in the Europa League or Champions League.