Atleti were ahead inside 23 seconds, the fastest goal in the Europa League so far this season, after Antoine Griezmann teed up Koke to fire past Rui Patricio following a defensive lapse from Sebastian Coates.
The hosts almost doubled their lead moments later when Diego Godin brought a save out of Patricio as Sporting struggled to gain a foothold in the game during the early exchanges.
Coates and Bas Dost then squandered opportunities to bring Sporting level before Griezmann fired another effort wide of the mark.
However, the Frenchman added to Atletico's lead when a mistake from Jeremy Mathieu put the forward in acres of space and he duly slotted past Patricio.
Los Rojiblancos nearly put the tie beyond the reach of the Liga Nos outfit when Diego Costa found himself one on one with Patricio but failed to finish.
Sporting almost snatched an away goal in stoppage time when after Jan Oblak pushed Bryan Ruiz's initial effort into the path of Fredy Montero, only for the substitute to blaze over from very short range.
The return leg takes place in Lisbon on April 12.
ATLETICO MADRID (4-4-2): Oblak; Hernandez, Godin, Savic, Juanfran; Koke, Gabi, Niguez, Correa (Gameiro 53'); Griezmann (Vitolo 90'), Costa (Partey 87')
SPORTING LISBON (4-2-3-1): Patricio; Piccini, Coates, Mathieu, Coentrao (Ribeiro 80'); Carvalho (Acuna 45'), Battaglia; Ruiz, Fernandes (Montero 87'), Martins; Dost