The Portugal international slotted home Alex Sandro's pinpoint pass 11 minutes into the second half to earn Porto victory in a match of few clearcut chances at the Estadio do Dragao.
The defeat was Malaga's first in their maiden Champions League campaign, but Manuel Pellegrini's men will be hopeful of turning things round at La Rosaleda, where they beat both AC Milan and Zenit St Petersburg in the group stages.
Two-time former European champions Porto will also be optimistic about their chances of going through to the quarter-finals, although they would have preferred a bigger advantage for the trip to Andalusia.
Vitor Pereira's hosts dominated the first half in terms of possession and territory, but created little to trouble visiting goalkeeper Willy Caballero.
The majority of Porto's efforts before the break were off-target, although Marat Izmailov did bring a diving save out of Caballero in the fourth minute.
Porto's next two chances saw Fernando and Silvestre Varela head Moutinho corners just wide before Caballero was called into action again on the half-hour mark to comfortable gather an optimistic Fernando shot.
At the other end Malaga only ventured deep into Porto territory sporadically as the respective defences - the tightest in the Portuguese and Spanish leagues this season - held the upper hand.
The home side would have been disappointed not to have worked Caballero more in the first period, but they came out strongly at the start of the second half and took just six minutes to fashion the best chance of the game so far.
Sandro sent over a cross from the left and the stretching Izmailov almost managed to turn it into the net, despite not getting a clean connection on his half-volley.
That was a major let-off for Malaga, but they were not so fortunate five minutes later as 1987 and 2004 champions Porto took the lead through Moutinho following more good work from Sandro.
The Brazilian did well to create space before picking out his team-mate's run into the box with an inch-perfect pass between the Malaga defence and goalkeeper Caballero, which the highly-rated Moutinho clinically side-footed home first time.
That proved to be the only goal of the match as defences continued to dominate during the closing stages, leaving things finely poised for the second leg.