Substitute Saul Niguez buried the rebound from his saved second-half penalty to give Atletico Madrid a 1-0 win.
Diego Simeone, who removed Antoine Griezmann after a goalless first 45 minutes, will now turn his team's attention to Wednesday's (NZDT) crunch trip to Juventus in the UEFA Champions League.
The Rojiblancos take a 2-0 advantage into the second leg of that last-16 tie, along with an imposing five-match winning streak in all competitions.
Atletico was without two injured left-backs and the suspended Diego Godin but Jan Oblak went untested until Martin Braithwaite's tame attempt in the 33rd minute.
Leganes did succeed in limiting the host to long-range efforts, its nerviest moment of the first half coming when Kenneth Omeruo sliced over his own crossbar in clearing Jose Gimenez's header.
Simeone, who left the in-form Alvaro Morata on the bench, surprisingly withdrew Griezmann at the interval, though his gamble was justified in the 50th minute.
Omeruo tripped Angel Correa in the box and midfielder Saul, one of two half-time changes, tucked away the loose ball after Andriy Lunin blocked his weak spot-kick.
Thomas Partey almost doubled the margin with deflected shot that dipped against the crossbar, before goalkeeper Lunin – on loan at Leganes from Real Madrid – tipped a Thomas Lemar free-kick against the upright.
Atletico encountered few concerns at the other end as a fifth straight clean sheet helped move it eight points ahead of Real Madrid, which meets Valladolid on Monday (NZDT).