Atletico's 2-0 win over Celta Vigo on Sunday (NZST) saw them move five points clear of third-placed Madrid, which had to rely on the in-form Karim Benzema to salvage a draw in a rare Tuesday outing.
Jonathan Silva's goal had given Leganes a deserved lead late in the first half, but Benzema drew his side level with his 18th LaLiga goal of the season six minutes after the restart.
Youssef En-Nesyri thought he had clinched a famous win for Leganes late on, but the offside flag sparred Madrid's blushes in what was a frustrating outing for the visitor.
Zidane saw his team make a break start, Marco Asensio failing to direct a close-range effort either side of Ivan Cuellar after 10 minutes.
Madrid should have been made to pay four minutes later, only for Martin Braithwaite to head wide from three yards out after getting the better of Nacho, playing in a defence minus the services of the injured Sergio Ramos.
But Madrid was punished on the stroke of half-time, Braithwaite teeing up Silva, who gave Keylor Navas little chance with a precise finish to the goalkeeper's right.
Leganes' lead was short-lived, though, Benzema - who had been played in brilliantly by Luka Modric - tucking home at the second attempt from a tight angle following a fine initial save from Cuellar.
Substitute En-Nesyri was rightly flagged offside as Leganes pushed for a winner, with Cuellar on top form at the other end to deny Marcelo and ensure a well-deserved point against their illustrious city rival.