Madrid boss Zinedine Zidane gambled on the strength of his squad ahead of a mammoth 18 days which sees the European champions welcome Atletico Madrid and Barcelona to the Santiago Bernabeu and also meet old foes Bayern Munich in the Champions League quarter-finals.
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However, the Frenchman was rewarded as the likes of Marco Asensio, James Rodriguez and Morata took their chance to shine.
As well as their slender lead, Real also have a game in hand over Barcelona.
"It is not taking a risk, I have a great squad," said Zidane. "I am always asked about the reserves and the starters, but we are all in the same boat. We are doing great things together, but we still have a long way to go and we will need every player."
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Asensio's storming run set up the opener for Rodriguez on 15 minutes as he weaved past three Leganes defenders before squaring for the Colombian to tap home his sixth goal of the season.
Morata's looping header and then calm finish into the top corner from Mateo Kovacic's pass looked to have put Madrid out of sight inside 23 minutes.
Yet, on Real's first ever La Liga visit to Butarque, the hosts had something to celebrate before half-time as Gabriel Pires and Luciano Neves took advantage of some slack Madrid defending to cut the deficit to 3-2 before half-time.
The visitors quickly restored their two-goal cushion just three minutes into the second-half, though, when Leganes captain Martin Mantovani contrived to punch the ball into his own net.
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