Captain Sergio Ramos gave the floundering European champions the lead from the penalty spot shortly before halftime at a sparsely attended Santiago Bernabeu.
Lucas Vazquez doubled the lead midway through the second half after a mix up between the visiting defence and goalkeeper Ivan Cuellar.
Brazilian teenager Vinicius Jr brought the crowd to its feet with an outrageous volley to further stretch Madrid's lead in the 78th minute, giving Santiago Solari's side a huge advantage heading into next Wednesday's return leg.
"Things haven't been going our way and we haven't been getting the right results, we were feeling angry and we unleashed that on the pitch," said Real defender Nacho.
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Fans stayed away from Santiago Bernabeu on Wednesday after Sunday's shock defeat by Real Sociedad left them 10 points adrift of leaders Barcelona in La Liga.
Solari, who has faced criticism for the team's drab start to 2019, also said the team felt a sense of release after the victory after the Sociedad defeat and last week's 2-2 draw at Villarreal.
"Real Madrid always need to win and always need to score, we came into this game after a match in which we deserved to score but didn't so obviously this result liberates us," Solari added.
"We played very well, we were solid and we deserved this result against a team that was very organised."
(Reporting by Richard Martin, editing by Pritha Sarkar)
