The visitors began brightly against the Serie A outfit and, five minutes in, Gelson Martins's cross from the left flashed across the face of goal.
On seven minutes, Cagliari stalwart Andrea Cossu was substituted in a symbolic move which heralded his retirement from football, thus giving him a chance to say his goodbyes in front of the home faithful.
The Rossoblu then came close to opening the scoring in the 21st minute, Diego Farias connecting with a header but finding the wrong side of the post, while Jan Oblak had to be alert to force a corner four minutes later.
Despite being given a tough game in the opening exchanges, Atletico would go on to score what turned out to be the winner just before the half-hour mark, with Martins forcing a save from Alessio Cragno which was buried home on the rebound by Borja Garces.
Although the Sardinians held their own for much of the game and even struck the woodwork in the second half through Alessandro Deiola, Diego Simeone's side always looked the more threatening and were unlucky not to end the game with a higher goal tally.
CAGLIARI (4-3-1-2): Cragno (Aresti 45'); Farago (Dessena 46'), Ceppitelli (Andreolli 45'), Romagna (Pisacane 45'), Lykogiannis (Pajac 45'); Castro (Colombatto 67'), Cigarini (Cerri 67'), Cossu (Barella 8', Padoin 33'); Ionita (Deoila 45'); Farias (Sau 45'), Pavoletti (Han 45')
ATLETICO MADRID (4-4-2): Oblak (Adan 45'), Juanfran (Mollejo 45'), Godin (Savic 45'), Gimenez (Montero 45'), Luis (Olabe 45'), Koke (Carro 59'), Saul (Rodri 59'), Lemar (Munoz 59'), Correa (Arias 45'), Gelson (Solano 59'), Borja (Munoz 67')