Antoine Griezmann - back in the side after missing the last two league games through suspension - scored the only goal of the night as Atletico got off to a winning start in their new home, climbing up to third in the table as a result.
Malaga, meanwhile, are still looking for their first La Liga points of the season having lost all four of their matches so far this term to prop up the table.
The occasion was marked with huge celebrations beforehand and fireworks around the ground, but it took a while for the action on the field to ignite as the two sides played out a tense and tight first half.
It was Malaga who came closest to breaking the deadlock in that opening 45 minutes, but Jan Oblak ensured that he would not concede the first goal at the new stadium when he denied Borja Baston at the near post.
The moment all the home fans had been waiting for finally arrived shortly after the hour mark, though, and fittingly it was Griezmann who provided it with a clinical low first-time finish into the bottom corner after good work from Angel Correa on the right flank.
Atletico won every La Liga match Griezmann scored in at the Vicente Calderon, and there were not many signs of that record ending at the new home as Malaga struggled to come up with a response.
The visitors did almost nick a point in the final minute, though, as Diego Rolan worked his way into the box before creating space to shoot, but once again Oblak was equal to the test.
Ultimately, Griezmann's historic goal proved to be the difference as Atletico ended a run of back-to-back goalless draws in their first home game of the new campaign.