Porto enjoyed most of the possession but had to wait until the second half to break the deadlock.
Brazilian left-back Alex Sandro slid a pinpoint pass into the area that Moutinho coolly side-footed in after 56 minutes for the Portuguese league leaders.
Television replays showed Moutinho was offside but the goal was given despite strong appeals from the Malaga players.
"This was a good result. We dominated from beginning to end," Moutinho told Portuguese radio.
"I looked to the referee to check [for offside] but I saw everyone was celebrating so I did too."
Malaga, fourth in Spain's top flight, defended resolutely in the first half but were innocuous up front with Roque Santa Cruz and Julio Baptista kept quiet by Porto's back four.
"We gave Malaga no room to think. The only reason why I am not truly satisfied is because we did not make it 2-0 which would have better reflected what happened in the match," said Porto coach Vitor Pereira.
Pereira and opposite number Manuel Pellegrini said before the game they expected plenty of attacking football but, in the first half at least, the show fell short of expectation.
MOUTINHO MAGIC
In the second period Moutinho, 26, showed just why he is so coveted by Europe's big-spending teams.
With a battery of scouts in the stands, he dictated the pace of play, recovered dozens of lost balls and also found the energy to show up in the box.
"Losing is never a good thing but losing 1-0 is the best we could have hoped for," said Malaga defender Martin Demichelis.
"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 [on March 13]. We definitely have a chance to turn it around."
Porto's top marksman, Colombian Jackson Martinez, shared the view of Demichelis.
"The next match will be much harder. They have a very strong defence," he said.
