Goals from Ferland Mendy – his first for the club – and Karim Benzema restored Madrid's four-point advantage over Barcelona with two games remaining.
Mendy slammed home a brilliant finish from a tight angle to become the 21st Madrid player to score in LaLiga this season, while Benzema increased his top-flight tally this term to 19 as he made it 2-0.
Although Darwin Machis pulled one back five minutes into the second half, Madrid survived a couple of late scares to make it nine straight victories and edge closer to a 34th LaLiga title.
Mendy won the penalty that put Madrid on their way to a 2-0 victory over Deportivo Alaves last time out and he got them off to a great start again, beating Victor Diaz for pace and smashing into the roof of the net from an acute angle in the 10th minute.
Benzema doubled the advantage following a swift counter-attacking move six minutes later, the Frenchman allowed time and space by Diaz to shift the ball onto his right foot and pick out the far corner.
Granada switched to a back four and quickly tested Thibaut Courtois, but Domingos Duarte's header was kept out of the bottom-right corner.
Benzema had a powerful shot tipped over by Rui Silva before half-time and Granada reduced the deficit shortly after the restart, Machis firing under Courtois after Yangel Herrera caught Casemiro in possession.
Zinedine Zidane responded to Granada's improvement by sending Rodrygo and Marco Asensio on for Federico Valverde and Isco just after the hour mark, with Madrid sitting back and consolidating.
Substitute Antonin had an acrobatic volley kept out by Courtois before Ramon Azeez saw his 85th-minute effort blocked on the line by returning captain Sergio Ramos, ensuring the visitors secured three valuable points.