James Rodriguez put Real ahead with a tap in at the 15th minute, at Estadio Municipal de Butarque in Madrid outskirts, before a Morata header and powerful strike, within five minutes made it 3-0 in the first 23 minutes of the game.
Leganes responded as Gabriel’s close-range finish and a Luciano strike reduced the deficit to one, all within two minutes.
But a Morata header in the 48th minute deflected in off Leganes captain, Martin Mantovani to seal victory for Real.
The win takes Zinedine Zidane’s side two points clear of Barcelona, who had earlier on Wednesday gone top after they beat Sevilla 3-0.
Lionel Messi was back in the side after serving a match ban. He scored twice as Barcelona brushed aside Sevilla to keep up the pressure on Real Madrid in the La Liga title race.
With the 4-2 victory at Leganes, Zinedine Zidane’s Real Madrid side have made it 203 competitive goals for the season.
James was on hand to break the deadlock at Butarque, with the side’s 200th goal of the campaign.
It has taken the Whites 73 games to reach this milestone, meaning that the team has averaged 2.7 goals per game.
These 203 strikes are made up 141 goals in LaLiga, 31 in the Champions League, 22 in the Copa del Rey, six in the Club World Cup and three in the UEFA Super Cup.
Zidane’s record in these 73 games reads 54 wins, 14 draws and five defeats.
