Atletico's midweek defeat to Chelsea appeared to have altered Diego Simeone's thinking as the coach switched formations on the road, and it proved difficult for the visitors to adjust in the opening stages.
In what proved to be a testing first half for both the teams and those watching, Atletico's only memorable chance came when Saul struck a speculative effort from distance, which produced a good save from Ivan Cuellar who saw the shot late through bodies.
Madrid failed to improve in the second half and they were almost behind when Nabil El Zhar found space inside the box, but Jan Oblak proved equal to it as the Atletico stopper punched clear with his fists.
As the game wore on, it looked as though Leganes might be the side to find a winner, and that goal almost came when El Zhar let fly again from range, only to see a diving Oblak tip his effort away from the top corner.
Such was Atletico's bluntness going forward, it took a standout effort from centre-back Diego Godin to next test the Leganes stopper, as the Uruguayan defender produced an adroit header that had Ivan Cuellar scrambling across his goal.
Leganes continued to hunt with confidence in the dying embers of the contest and Oblak had to be alive again to turn away a cross from Nordin Amrabat with El Zhar lurking, leaving Atletico to narrowly escape from what might have been a surprising defeat.