Wales forward Gareth Bale produced an acrobatic finish from close range on the volley to put Madrid ahead against their neighbours in the eighth minute of the game, narrowly beating the offside trap despite protests from the visiting players.
Borja Mayoral doubled their lead right at the end of the first half by stabbing in from a metre out. Again Leganes appealed for offside but the goal was eventually allowed to stand after the referee consulted with his assistant.
Leganes were unfortunate to go two goals down at the interval after coming to close to scoring on three occasions, including Watford loanee Nordin Amrabat striking the crossbar.
They eventually pulled a goal back in the 66th minute when Darko Brasanac knocked a cutback from Amrabat into an empty net.
Leganes forward Gabriel was sent off after the final whistle for reacting furiously to the referee for ending the game just as he was shaping to shoot at goal from outside the area.
Real are third in the league on 71 points, 12 behind runaway leaders Barcelona and one behind second-placed Atletico Madrid.
Atletico visit Alaves on Sunday while Barca play at Deportivo La Coruna, where a point will see the Catalans become Liga champions for a 25th time.
Zidane excluded Ronaldo, captain Sergio Ramos and Raphael Varane from the squad and left Luka Modric, goalkeeper Keylor Navas and influential left back Marcelo on the bench.
He later brought on midfielder Toni Kroos and winger Marco Asensio, who scored the winning goal in the 2-1 victory at Bayern in Wednesday's first leg.
(Reporting by Richard Martin; Editing by Christian Radnedge)
