Joao Moutinho turned in a midfield masterclass to score the only goal as Malaga once again lost in Oporto to put their Champions League hopes in doubt.
Champions League: Moutinho the difference maker as Malaga lose to Porto
The hosts dominated the opening period but failed to create a clear opening until six minutes after the break when Alex Sandro's fine pass was swept past Willy Caballero first time by Moutinho.
Porto were then happier to hold on to their advantage than go in search of a second and with Malaga unable to muster any sort of response the tie is delicately balanced heading into the return at La Rosaleda in three weeks' time.
"Losing is never a good thing but losing 1-0 is the best we could have hoped for," Martin Demichelis, the Malaga defender, said afterwards.
"It was a shame we came up against fantastic opponents who knew how to pressure us and controlled the ball well.
"We couldn't be the team we usually are but we'll give it our all in Malaga and try to put them under the same kind of pressure in the second leg. We definitely have a chance to turn it around."
Malaga's only previous defeat in European competition had come in the city of Oporto to Boavista in 2003 and they seemed set to suffer a similar fate throughout a first-half which the hosts dominated.
Marat Izmailov was handed a start ahead of James Rodriguez as the latter continues his return from injury and the Russian tested Caballero with a low drive just four minutes in.
However, for all their possession Porto failed to force the Argentine into another save for the rest of the opening period.
Twice Fernando headed just off target from Moutinho corners before Danilo and Izmailov also fired wide of Caballero's right-hand post.
Izmailov was again off the mark as he slid in at the back post moments after the break but ironically it was when the visitors had been enjoying their best spell of possession when Porto eventually found a way through.
A lovely pass from Sandro split the Malaga defence wide open and Moutinho timed his run perfectly to slot confidently past Caballero.
Rodriguez then replaced Silvestre Varela and the Colombian nearly had an immediate effect as he curled a shot just wide two minutes later.
Manuel Pellegrini then also turned to his bench in search of a goal, but despite introducing an extra striker as Javier Saviola and Lucas Piazon replaced Julio Baptista and Manuel Iturra, Malaga still failed to create anything of note going forward.
And the Spanish side will have it all to do on homesoil if they are to reach the quarter-finals in their first ever Champions League campaign.