Manuel Pellegrini's side, on their first venture into Europe's top club competition, came back to beat Porto 2-1 on aggregate at a festive Rosaleda on Wednesday, but they struggled against a well-organised Espanyol.
Goalkeeper Willy Caballero, the rock upon which much of their success has been built this season, made a rare mistake when he fumbled a corner in the 49th minute and Diego Colotto volleyed the visitors in front against the run of play.
The hosts looked short on spark and were undone again in the 66th when Mubarak Wakaso burst down the left and crossed for Sergio Garcia to volley a superb second into the top corner.
Home fans continued to sing and applaud their side despite the setback, but the defeat left Malaga, who have not won in their last four league outings, in sixth place with 44 points and 10 games left to play.
Real Sociedad and Valencia both won on Saturday to climb above them into fourth and fifth respectively.
Sociedad thumped Real Valladolid 4-1 to move on to 47 points, and Valencia beat 10-man Real Betis 3-0 to climb on to 45.
Espanyol had 33.6% of possession. Periquitos had five shots, all of which were on target.
Joan Verdú had two shots for Espanyol, more than any of his team-mates.
With a ball control percentage of 66.4%, Málaga played an effective brand of possession football despite the loss.
Málaga's players linked up for 499 passes and 29 crosses.
The three attempts by Roque Santa Cruz were the most of any Málaga player.
The combination of Jérémy Toulalan to Jesús Gámez was the most common during the match, as the two players connected 21 times.