The French international, restored to the side after a two-game La Liga ban, swept home Angel Correa's cross on the hour mark to move Atletico up to third in the table.
Atletico remain four points adrift of Barcelona, though, as Paulinho scored his first Barca goal six minutes from time to continue their 100 percent record in a 2-1 win at Getafe.
"I'm delighted to score the first goal in this magnificent stadium and hopefully it is the first of many," Griezmann told Bein Sports Spain.
"For me it is the best stadium I have played in, and I don't just say that because it is my club."
Atletico boss Diego Simeone had called on fans to recreate the intimidating atmosphere of the Vicente Calderon by turning their new home into a "pressure cooker."
The noise matched the pre-match pomp as Spain's royal air force took part in a flyover, whilst the match ball was delivered by paragliders.As a player or a coach I have never seen anything like it," said Simeone.
"The memory will live with me for the rest of my life.All the Atletico flags flying, the fans involvement, I wanted to go on and play!"
Spanish king Felipe VI, an Atletico fan, was also in attendance, but after all the pre-match fanfare, there wasn't much for the crowd to get enthused about in the opening 45 minutes.
Correa had Atletico's only two clear chances of the half as he blazed over and straight at Roberto Jimenez.
At the other end Jan Oblak was forced into a fine save from ex-Atletico striker Borja Baston as Malaga broke dangerously.
Atletico started the second period brighter as Roberto denied Koke and Saul Niguez before the deadlock was broken on the hour mark.
Correa burst clear down the right and his low cross was expertly guided inside the near post by Griezmann on his weaker right foot.
Malaga had one late chance to rain on Atletico's parade two minutes from time, but Oblak was again up to the task to turn Diego Rolan's fierce effort over the bar.