The Colchoneros managed to edge out the tough-looking Salzburg side.
Atletico Madrid have won their final group stage fixture against Salzburg, thus advancing to the knockouts.
The game was touted as an important clash for both the sides to keep their Champions League alive, however, it was Atletico who had the last laugh.
The hosts spelled trouble to Diego Simeone’s side after hitting the crossbar at the start of the game while they kept Atletico’s defence at fence throughout the game.
Mario Hermoso’s header from the set-piece right before the first half released the pressure off the visitors while taking a big leap towards qualification for the knockouts.
Belgian winger Yannick Carrasco put the game to bed after scoring the second goal in the 86th minute, hitting the nets with a volley from Angel Correa’s cross.
Carraco has been instrumental to Atletico since his return as he had recently scored the winning goal against Barcelona.
Atletico’s robust defence helped Simeone weather a major storm as Jan Oblak kept another clean sheet.
Elsewhere, Salzburg, who had gained the reputation for causing trouble to the opponents throughout the season, had their Champions League journey come to an end.
Los Rojiblancos have been unstoppable in La Liga this season, currently leading the table with no defeats. However, their UCL form was questioned after a huge defeat against Bayern Munich in the opening day and followed by two more draws.