Atletico looked to be in danger of dropping its first points of the season on, having beaten Getafe in its season opener, but substitute Vitolo finished coolly 19 minutes from time to seal the victory.
Alvaro Morata was one of few players to look even remotely threatening in the first half, with proceedings not offering much excitement until the second half, which saw a flurry of action early on.
Both sides struck the frame of the goal and Joao Felix wasted a glorious opportunity, but the €120million signing made amends by setting Vitolo up for the winner.
Atletico shaded a generally drab first period, with Morata the only player to go close.
He first shot wide from Koke's low cross in the third minute and half an hour later latched on to Kieran Trippier's lofted ball only to be thwarted by the approaching Juan Soriano as he attempted to prod an effort over the goalkeeper.
The second half began in much livelier fashion – Joao Felix spurning a glorious chance in the 50th minute when needlessly attempting a scissor-kick from 12 yards with the goal gaping.
Leganes went even closer soon after when Jonathan Silva's free-kick struck the crossbar, before Koke nudged a Morata cross onto the post.
Atletico eventually wrapped up the win in the 71st minute, as Joao Felix drove in from the right, picked out Vitolo in the box and the forward swept home confidently with his left foot.