Head coach Iñigo Pérez hailed his side's response to going a goal down as the defining feature of the performance.
"The real merit is bouncing back from the first goal, given where we've come from, and continuing to play the way they played. A complete performance against a very difficult opponent — I'm satisfied," Pérez said, in what he described as a psychological turning point for a Villarreal side that had endured a difficult start to the campaign.
"You have to bear in mind that we started losing, and at that moment doubts could easily have crept in, fear of another defeat repeating itself. Now I'm very happy, both with the win and the way we got it. They showed calmness and mental strength."
Pérez also addressed Santi Comesaña's injury, which forced the midfielder off during the match.
"If Santi leaves the pitch of his own accord, it's because he's in pain, that he's hurt, and we'll see what the tests show. But it was an important loss for the game — hopefully it isn't serious," he said.
Asked about his side's late defensive shape, with three central defenders protecting a one-goal lead, Pérez explained the reasoning.
"We wanted a three-against-two at the back, and often, without sitting too deep, that back-five-plus-four set-up creates mistakes from the opponent that let you transition," he said.
For Málaga, the result underlined the gulf still facing newly promoted sides in La Liga. Head coach Juan Francisco Funes conceded his team remain some way off matching sides like Villarreal.
"We tried to reinforce the midfield. From the goal onwards we wanted to keep being protagonists, but they were at a great level. You live with the feeling that we're missing that little step to match them," he said. "It was difficult to break their high press and end up with more goals."
Funes pointed to Villarreal's second goal as the moment the game turned decisively away from Málaga.
"The goal that activates them is theirs. Everything they've achieved is a result of that shift. Villarreal pushed us back into a defensive position," he said, while insisting his squad's frustration should not become resignation. "We've reached the most demanding category, but we have to keep taking steps. Frustration can't make us give up. We have a huge margin for growth."