Atletico's 2-0 win over Celta Vigo on Saturday saw them move five points clear of third-placed Madrid, who had to rely on the in-form Karim Benzema to salvage a draw in a rare Monday 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 visitors.
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 were 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 rivals.
What does it mean? Zidane's revival takes a hit
Three successive wins had put Madrid well back in the hunt for second place, though a defeat on the road at Valencia, followed up by another lacklustre display against Leganes in their next away outing, has left their hopes in the balance.
Benzema gets Los Blancos out of trouble
Madrid's number nine has been a rare bright spot in a frustrating season and despite being denied by Cuellar at the first attempt, he kept his cool to convert the rebound and continue his impressive scoring streak.
Madrid's defence lacking leadership without Ramos
With Ramos sidelined with a calf injury, neither Nacho or Raphael Varane will have done much to impress Zidane, with the lively Braithwaite too easily getting the better of the pair on occasions.
Madrid welcome Athletic Bilbao to Santiago Bernabeu on Sunday, while Leganes travel to relegation-threatened Villarreal.