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Joao Moutinho's second-half goal was enough to give Porto a 1-0 win over Malaga in a cagey first-leg at the Estadio do Dragao on Tuesday.
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, although replays showed the Portuguese international may have been in an offside position.
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.
"Whether it is a good result or not we will see at the end of 180 minutes," Malaga coach Manuel Pellegrini told Spanish TV station TVE.
"To lose is never good but losing by just the one goal is the best thing we can take from the game.
"For all the possession Porto had they didn't create many clear-cut chances and even the goal itself is offside.
"You have to give credit to Porto for the way they pressed us all over the pitch, but we have to apply the same pressure in Malaga.
"We can still turn the tie around at La Rosaleda. We have demonstrated this year that we can compete with anyone," added Pellegrini.
Porto boss Vitor Pereira meanwhile was much happier with his men but lamented not killing the tie off with a second goal.
"We played a complete game, we dominated and pressed them which is what I like to see," he told reporters.
"We were playing a great team and we completely took the initiative from them, but it was a shame not to have scored the second goal."
Malaga's only previous defeat in European competition had also come in the city of Porto, to Boavista in 2003, and they slipped to a similar fate after failing to have a single shot on target throughout the 90 minutes.
Marat Izmailov was handed a start ahead of James Rodriguez as the latter continued 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 that Porto eventually found a way through.
A lovely pass from Alex Sandro split the Malaga defence wide open and Moutinho was allowed to run on and slot past Caballero first time despite just being goal-side of Martin Demichelis as the ball was played.
And there was very little by way of goalmouth action in the final half hour as both sides seemed content for the tie to be settled in the south of Spain on March 13.